Solitons in nonlinear lattices

Reviews of Modern Physics

Volumn 83, Issue 1, 2011, Pages 247-305

  Kartashov, Yaroslav V ^a   Malomed, Boris A ^b   Torner, Lluis ^a  

^a UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

^b TEL AVIV UNIVERSITY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

BASIC PROPERTIES; BLOCH MODES; EXPERIMENTAL STUDIES; FINITE THRESHOLDS; FUNDAMENTAL PROPERTIES; LINEAR LATTICES; NON-LINEARITY; NONLINEAR LATTICES; NONLINEAR WAVES; OPTICAL MEDIA; PERIODIC MODULATION; PHYSICAL SYSTEMS; PLASMONICS; SPATIAL MODULATIONS; THEORETICAL PREDICTION; THREE DIMENSIONS;

BOSE-EINSTEIN CONDENSATION; CONDENSATION; NONLINEAR OPTICS; OPTICAL MATERIALS; PHOTONIC CRYSTALS; STATISTICAL MECHANICS; SURVEYS;

SOLITONS;

EID: 79958829572     PISSN: 00346861     EISSN: 15390756     Source Type: Journal    
DOI: 10.1103/RevModPhys.83.247     Document Type: Article

References (343)

1. Abdelrahman, A., P. Hannaford, and K. Alameh, 2009, " Adiabatically induced coherent Josephson oscillations of ultracold atoms in an asymmetric two-dimensional magnetic lattice, " Opt. Express OPEXFF 1094-4087 17, 24358. 10.1364/OE.17.024358
2. Abdullaev, F., A. Abdumalikov, and R. Galimzyanov, 2007, " Gap solitons in Bose-Einstein condensates in linear and nonlinear optical lattices, " Phys. Lett. A 367, 149. PYLAAG 0375-9601 10.1016/j.physleta.2007.02.067
3. Abdullaev, F., A. Gammal, H.L.F. da Luz, and L. Tomio, 2007, " Dissipative dynamics of matter-wave solitons in a nonlinear optical lattice, " Phys. Rev. A 76, 043611. PLRAAN 1050-2947 10.1103/PhysRevA.76.043611 (Pubitemid 47569966)
4. Abdullaev, F.K., Y.V. Bludov, S.V. Dmitriev, P.G. Kevrekidis, and V.V. Konotop, 2008, " Generalized neighbor-interaction models induced by nonlinear lattices, " Phys. Rev. E PLEEE8 1539-3755 77, 016604. 10.1103/PhysRevE.77.016604 (Pubitemid 351169681)
5. Abdullaev, F.K., R.M. Galimzyanov, M. Brtka, and L. Tomio, 2009, " Soliton dynamics at an interface between a uniform medium and a nonlinear optical lattice, " Phys. Rev. E PLEEE8 1539-3755 79, 056220. 10.1103/PhysRevE.79.056220
6. Abdullaev, F.K., A. Gammal, M. Salerno, and L. Tomio, 2008, " Localized modes of binary mixtures of Bose-Einstein condensates in nonlinear optical lattices, " Phys. Rev. A 77, 023615. PLRAAN 1050-2947 10.1103/PhysRevA.77.023615 (Pubitemid 351393352)
7. Abdullaev, F.K., A. Gammal, and L. Tomio, 2004, " Dynamics of bright matter-wave solitons in a Bose-Einstein condensate with inhomogeneous scattering length, " J. Phys. B JPAPEH 0953-4075 37, 635. 10.1088/0953-4075/37/3/009
8. Abdullaev F.K., and J. Garnier, 2005, " Propagation of matter-wave solitons in periodic and random nonlinear potentials, " Phys. Rev. A 72, 061605(R). PLRAAN 1050-2947 10.1103/PhysRevA.72.061605 (Pubitemid 43272769)
9. Abdullaev, F.K., V.V. Konotop, M. Salerno, and A.V. Yulin, 2010, " Dissipative periodic waves, solitons, and breathers of the nonlinear Schrödinger equation with complex potentials, " Phys. Rev. E PLEEE8 1539-3755 82, 056606. 10.1103/PhysRevE.82.056606
10. Adhikari, S.K., B.A. Malomed, L. Salasnich, and F. Toigo, 2010, " Spontaneous symmetry breaking of Bose-Fermi mixtures in double-well potentials, " Phys. Rev. A 81, 053630. PLRAAN 1050-2947 10.1103/PhysRevA.81.053630
11. Agrawal, G.P., 1995, Nonlinear Fiber Optics (Academic Press, San Diego).
12. Alfassi, B., C. Rotschild, O. Manela, M. Segev, and D.N. Christodoulides, 2007, " Nonlocal surface-wave solitons, " Phys. Rev. Lett. 98, 213901. PRLTAO 0031-9007 10.1103/PhysRevLett.98.213901 (Pubitemid 47139653)
13. Anderson, M.H., J.R. Ensher, M.R. Matthews, C.E. Wieman, and E.A. Cornell, 1995, " Observation of Bose-Einstein condensation in a dilute atomic vapor, " Science 269, 198. SCIEAS 0036-8075 10.1126/science.269. 5221.198
14. Anker, T., M. Albiez, R. Gati, S. Hunsmann, B. Eiermann, A. Trombettoni, and M.K. Oberthaler, 2005, " Nonlinear self-trapping of matter waves in periodic potentials, " Phys. Rev. Lett. 94, 020403. PRLTAO 0031-9007 10.1103/PhysRevLett.94.020403 (Pubitemid 40620121)
15. Avelar, A.T., D. Bazeia, and W.B. Cardoso, 2010, " Modulation of breathers in the three-dimensional nonlinear Gross-Pitaevskii equation, " Phys. Rev. E PLEEE8 1539-3755 82, 057601. 10.1103/PhysRevE.82.057601
16. Baizakov, B.B., B.A. Malomed, and M. Salerno, 2003, " Multidimensional solitons in periodic potentials, " Europhys. Lett. 63, 642. EULEEJ 0295-5075 10.1209/epl/i2003-00579-4 (Pubitemid 37089624)
17. Baizakov, B.B., B.A. Malomed, and M. Salerno, 2004, " Multidimensional solitons in a low-dimensional periodic potential, " Phys. Rev. A 70, 053613. PLRAAN 1050-2947 10.1103/PhysRevA.70.053613 (Pubitemid 40072999)
18. Beeckman, J., H. Azarinia, and M. Haelterman, 2009, " Countering spatial soliton breakdown in nematic liquid crystals, " Opt. Lett. 34, 1900. OPLEDP 0146-9592 10.1364/OL.34.001900
19. Belmonte-Beitia, J., and G.F. Calvo, 2009, " Exact solutions for the quintic nonlinear Schrödinger equation with time and space modulated nonlinearities and potentials, " Phys. Lett. A 373, 448. PYLAAG 0375-9601 10.1016/j.physleta.2008.11.056
20. Belmonte-Beitia, J., V.V. Konotop, V.M. Pérez-García, and V.E. Vekslerchik, 2009, " Localized and periodic exact solutions to the nonlinear Schrödinger equation with spatially modulated parameters: Linear and nonlinear lattices, " Chaos Solitons Fractals 41, 1158. CSFOEH 0960-0779 10.1016/j.chaos.2008.04.057
21. Belmonte-Beitia, J., and D. Pelinovsky, 2009, " Bifurcation of Gap Solitons in Periodic Potentials With a Sign-Varying Nonlinearity Coefficient, " arXiv:0906.2501v1.
22. Belmonte-Beitia, J., V.M. Perez-Garcia, and V. Brazhnyi, 2009, " Solitary Waves in Coupled Nonlinear Schrödinger Equations with Spatially Inhomogeneous Nonlinearities, " arXiv:1001.2425.v1.
23. Belmonte-Beitia, J., V.M. Perez-Garcia, and V. Vekslerchik, 2007, " Lie symmetries and solitons in nonlinear systems with spatially inhomogeneous nonlinearities, " Phys. Rev. Lett. 98, 064102. PRLTAO 0031-9007 10.1103/PhysRevLett.98.064102 (Pubitemid 46220449)
24. Belmonte-Beitia, J., V.M. Perez-Garcia, V. Vekslerchik, and V.V. Konotop, 2008, " Localized nonlinear waves in systems with time- and space-modulated nonlinearities, " Phys. Rev. Lett. 100, 164102. PRLTAO 0031-9007 10.1103/PhysRevLett.100.164102 (Pubitemid 351590587)
25. Benton, C.J., A.V. Gorbach, and D.V. Skryabin, 2008, " Spatiotemporal quasisolitons and resonant radiation in arrays of silicon-on-insulator photonic wires, " Phys. Rev. A 78, 033818. PLRAAN 1050-2947 10.1103/PhysRevA.78.033818
26. Berge, L., 1998, " Wave collapse in physics: Principles and applications to light and plasma waves, " Phys. Rep. 303, 259. PRPLCM 0370-1573 10.1016/S0370-1573(97)00092-6
27. Birks, T.A., J.C. Knight, and P.S. Russell, 1997, " Endlessly single-mode photonic-crystal fiber, " Opt. Lett. 22, 961. OPLEDP 0146-9592 10.1364/OL.22.000961
28. Blank, E., and T. Dohnal, 2009, " Families of surface gap solitons and their stability via the numerical Evans function method, " arXiv:0910.4585v2.
29. Bloch, I., J. Dalibard, and W. Zwerger, 2008, " Many-body physics with ultracold gases, " Rev. Mod. Phys. 80, 885. RMPHAT 0034-6861 10.1103/RevModPhys.80.885
30. Blömer, D., A. Szameit, F. Dreisow, T. Schreiber, S. Nolte, and A. Tünnermann, 2006, " Nonlinear refractive index of fs-laser-written waveguides in fused silica, " Opt. Express 14, 2151. OPEXFF 1094-4087 10.1364/OE.14.002151
31. Bludov, Y.V., V.A. Brazhnyi, and V.V. Konotop, 2007, " Delocalizing transition in one-dimensional condensates in optical lattices due to inhomogeneous interactions, " Phys. Rev. A 76, 023603. PLRAAN 1050-2947 10.1103/PhysRevA.76.023603 (Pubitemid 47246900)
32. Bludov, Y.V., and V.V. Konotop, 2006, " Localized modes in arrays of boson-fermion mixtures, " Phys. Rev. A 74, 043616. PLRAAN 1050-2947 10.1103/PhysRevA.74.043616 (Pubitemid 44631120)
33. Bludov, Y.V., V.V. Konotop, and M. Salerno, 2009, " Rabi oscillations of matter-wave solitons in optical lattices, " Phys. Rev. A 80, 023623. PLRAAN 1050-2947 10.1103/PhysRevA.80.023623
34. Bludov, Yu.V., and V.V. Konotop, 2010, " Nonlinear patterns in Bose-Einstein condensates in dissipative optical lattices, " Phys. Rev. A 81, 013625. PLRAAN 1050-2947 10.1103/PhysRevA.81.013625
35. Bludov, Y.V., V.V. Konotop, and M. Salerno, 2011, " Linear superpositions of nonlinear matter waves in optical lattices, " Europhys. Lett. EULEEJ 0295-5075 93, 30003. 10.1209/0295-5075/93/30003
36. Borovkova, O.V., Y.V. Kartashov, and L. Torner, 2010, " Stabilization of two-dimensional solitons in cubic-saturable nonlinear lattices, " Phys. Rev. A 81, 063806. PLRAAN 1050-2947 10.1103/PhysRevA.81.063806
37. Bradley, C.C., C.A. Sackett, J.J. Tollett, and R.G. Hulet, 1995, " Evidence of Bose-Einstein condensation in an atomic gas with attractive interactions, " Phys. Rev. Lett. 75, 1687. PRLTAO 0031-9007 10.1103/PhysRevLett.75.1687
38. Brazhnyi, V.A., and V.V. Konotop, 2004, " Theory of nonlinear matter waves in optical lattices, " Mod. Phys. Lett. B 18, 627. MPLBET 0217-9849 10.1142/S0217984904007190 (Pubitemid 40292032)
39. Bronski, J.C., L.D. Carr, B. Deconinck, and J.N. Kutz, 2001, " Bose-Einstein condensates in standing waves: The cubic nonlinear Schrodinger equation with a periodic potential, " Phys. Rev. Lett. 86, 1402. PRLTAO 0031-9007 10.1103/PhysRevLett.86.1402 (Pubitemid 32873600)
40. Burger, S., K. Bongs, S. Dettmer, W. Ertmer, K. Sengstock, A. Sanpera, G.V. Shlyapnikov, and M. Lewenstein, 1999, " Dark solitons in Bose-Einstein condensates, " Phys. Rev. Lett. 83, 5198. PRLTAO 0031-9007 10.1103/PhysRevLett.83.5198
41. Burger, S., F.S. Cataliotti, C. Fort, F. Minardi, M. Inguscio, M.L. Chiofalo, and M.P. Tosi, 2001, " Superfluid and dissipative dynamics of a Bose-Einstein condensate in a periodic optical potential, " Phys. Rev. Lett. 86, 4447. PRLTAO 0031-9007 10.1103/PhysRevLett.86.4447 (Pubitemid 32471360)
42. Buryak, A.V., P. Di Trapani, D.V. Skryabin, and S. Trillo, 2002, " Optical solitons due to quadratic nonlinearities: From basic physics to futuristic applications, " Phys. Rep. 370, 63. PRPLCM 0370-1573 10.1016/S0370-1573(02)00196-5
43. Buse, K., 1997 a, " Light-induced charge transport processes in photorefractive crystals I: Models and experimental methods, " Appl. Phys. B APBOEM 0946-2171 64, 273. 10.1007/s003400050175
44. Buse, K., 1997 b, " Light-induced charge transport processes in photorefractive crystals II: Materials, " Appl. Phys. B APBOEM 0946-2171 64, 391. 10.1007/s003400050190
45. Cai, D., A.R. Bishop, and N. Gronbech-Jensen, 1996, " Perturbation theories of a discrete, integrable nonlinear Schrödinger equation, " Phys. Rev. E PLEEE8 1063-651X 53, 4131. 10.1103/PhysRevE.53.4131
46. Cardoso, W.B., A.T. Avelar, and D. Bazeia, 2010, " Modulation of breathers in cigar-shaped Bose-Einstein condensates, " Phys. Lett. A 374, 2640. PYLAAG 0375-9601 10.1016/j.physleta.2010.04.050
47. Cardoso, W.B., A.T. Avelar, D. Bazeia, and M.S. Hussein, 2010, " Solitons of two-component Bose-Einstein condensates modulated in space and time, " Phys. Lett. A 374, 2356. PYLAAG 0375-9601 10.1016/j.physleta.2010.03.065
48. Carpentier, A.V., J. Belmonte-Beitia, H. Michinel, and M.I. Rodas-Verde, 2008, " Laser tweezers for atomic solitons, " J. Mod. Opt. JMOPEW 0950-0340 55, 2819. 10.1080/09500340802209763
49. Carpentier, A.V., H. Michinel, D.N. Olivieri, and D. Novoa, 2010, " Continuous atom laser with Bose-Einstein condensates involving three-body interactions, " J. Phys. B JPAPEH 0953-4075 43, 105302. 10.1088/0953-4075/43/10/105302
50. Carpentier, A.V., H. Michinel, M.I. Rodas-Verde, and V.M. Pérez-García, 2006, " Analysis of an atom laser based on the spatial control of the scattering length, " Phys. Rev. A 74, 013619. PLRAAN 1050-2947 10.1103/PhysRevA.74.013619 (Pubitemid 44100030)
51. Carr, L.D., and J. Brand, 2004, " Pulsed atomic soliton laser, " Phys. Rev. A 70, 033607. PLRAAN 1050-2947 10.1103/PhysRevA.70.033607
52. Carr, L.D., C.W. Clark, and W.P. Reinhardt, 2000, " Stationary solutions of the one-dimensional nonlinear Schrödinger equation. I. Case of repulsive nonlinearity, " Phys. Rev. A 62, 063610; PLRAAN 1050-2947 10.1103/PhysRevA.62.063610 (Pubitemid 32076698)
53. Carr, L.D. C.W. Clark W.P. Reinhardt Phys. Rev. A Stationary solutions of the one-dimensional nonlinear Schrödinger equation. II. Case of attractive nonlinearity, 62, 063611 (2000). PLRAAN 1050-2947 10.1103/PhysRevA.62.063611 (Pubitemid 32076699)
54. Carretero-González, R., D.J. Frantzeskakis, and P.G. Kevrekidis, 2008, " Nonlinear waves in Bose-Einstein condensates: Physical relevance and mathematical techniques, " Nonlinearity 21, R139. NONLE5 0951-7715 10.1088/0951-7715/21/7/R01
55. Carretero-González, R., J.D. Talley, C. Chong, and B.A. Malomed, 2006, " Multistable solitons in the cubic-quintic discrete nonlinear Schrödinger equation, " Physica D (Amsterdam) 216, 77. PDNPDT 0167-2789 10.1016/j.physd.2006.01.022 (Pubitemid 44316683)
56. Centini, M., C. Sibilia, M. Scalora, G.D. Aguanno, M. Bertolotti, M.J. Bloemer, C.M. Bowden, and I. Nefedov, 1999, " Dispersive properties of finite, one-dimensional photonic band gap structures: Application to nonlinear quadratic interactions, " Phys. Rev. E PLEEE8 1063-651X 60, 4891 10.1103/PhysRevE.60.4891.
57. Centurion, M., M.A. Porter, Y. Pu, P.G. Kevrekidis, D.J. Frantzeskakis, and D. Psaltis, 2006 a, " Modulational instability in a layered Kerr medium: Theory and experiment, " Phys. Rev. Lett. 97, 234101. PRLTAO 0031-9007 10.1103/PhysRevLett.97.234101 (Pubitemid 44888131)
58. Centurion, M, M.A. Porter, P.G. Kevrekidis, and D. Psaltis, 2006 b, " Nonlinearity management in optics: Experiment, theory, and simulation, " Phys. Rev. Lett. 97, 033903. PRLTAO 0031-9007 10.1103/PhysRevLett.97. 033903 (Pubitemid 44100056)
59. Cerqueira, A.S. Jr., 2010, " Recent progress and novel applications of photonic crystal fibers, " Rep. Prog. Phys. 73, 024401. RPPHAG 0034-4885 10.1088/0034-4885/73/2/024401
60. Chávez Cerda, S., S.B. Cavalcanti, and J.M. Hickmann, 1998, " A variational approach of nonlinear dissipative pulse propagation, " Eur. Phys. J. D 1, 313. EPJDF6 1434-6060 10.1007/s100530050098 (Pubitemid 128063196)
61. 3 waveguide arrays, " Opt. Express 13, 4314. OPEXFF 1094-4087 10.1364/OPEX.13.004314 (Pubitemid 40899330)
62. Chen, P.Y.P., and B.A. Malomed, 2005, " A model of a dual-core matter-wave soliton laser, " J. Phys. B JPAPEH 0953-4075 38, 4221. 10.1088/0953-4075/38/23/005 (Pubitemid 41720757)
63. Chen, P.Y.P., and B.A. Malomed, 2006, " Stable circulation modes in a dual-core matter-wave laser, " J. Phys. B JPAPEH 0953-4075 39, 2803. 10.1088/0953-4075/39/12/014 (Pubitemid 43884557)
64. Chen, Z., H. Martin, E.D. Eugenieva, J. Xu, and A Bezryadina, 2004, " Anisotropic enhancement of discrete diffraction and formation of two-dimensional discrete-soliton trains, " Phys. Rev. Lett. 92, 143902. PRLTAO 0031-9007 10.1103/PhysRevLett.92.143902
65. Cheng, Y., 2009, " Effective potential of two coupled binary matter wave bright solitons with spatially modulated nonlinearity, " J. Phys. B JPAPEH 0953-4075 42, 205005. 10.1088/0953-4075/42/20/205005
66. Chin, C., R. Grimm, P. Julienne, and E. Tiesinga, 2009, " Feshbach Resonances in Ultracold Gases, " arXiv: 0812.1496.
67. Choi, D.I., and Q. Niu, 1999, " Bose-Einstein condensates in an optical lattice, " Phys. Rev. Lett. 82, 2022. PRLTAO 0031-9007 10.1103/PhysRevLett.82.2022
68. Chong, C., R. Carretero-González, B.A. Malomed, and P.G. Kevrekidis, 2009, " Multistable solitons in higher-dimensional cubic-quintic nonlinear Schrödinger lattices, " Physica D (Amsterdam) 238, 126. PDNPDT 0167-2789 10.1016/j.physd.2008.10.002
69. Christiansen, P.L., Y.B. Gaididei, V.K. Mezentsev, S.L. Musher, K.Ø. Rasmussen, J. Juul Rasmussen, I.V. Ryzhenkova, and S.K. Turitsyn, 1996, " Discrete localized states and localization dynamics in discrete nonlinear Schrödinger equations, " Phys. Scr. PHSTBO 0031-8949 67, 160 10.1088/0031-8949/1996/T67/032.
70. Christodoulides, D.N., and R.I. Joseph, 1988, " Discrete self-focusing in nonlinear arrays of coupled waveguides, " Opt. Lett. OPLEDP 0146-9592 13, 794. 10.1364/OL.13.000794
71. Claude, C., Y.S. Kivshar, O. Kluth, and K.H. Spatschek, 1993, " Moving localized modes in nonlinear lattices, " Phys. Rev. B PRBMDO 0163-1829 47, 14228. 10.1103/PhysRevB.47.14228
72. Cohen, O., G. Bartal, H. Buljan, T. Carmon, J.W. Fleischer, M. Segev, and D.N. Christodoulides, 2005, " Observation of random-phase lattice solitons, " Nature (London) NATUAS 0028-0836 433, 500. 10.1038/nature03267 (Pubitemid 40204302)
73. Conti, C., M. Peccianti, and G. Assanto, 2004, " Observation of optical spatial solitons in a highly nonlocal medium, " Phys. Rev. Lett. 92, 113902. PRLTAO 0031-9007 10.1103/PhysRevLett.92.113902
74. Cornish, S.L., S.T. Thompson, and C.E. Wieman, 2006, " Formation of bright matter-wave solitons during the collapse of attractive Bose-Einstein condensates, " Phys. Rev. Lett. 96, 170401. PRLTAO 0031-9007 10.1103/PhysRevLett.96.170401 (Pubitemid 43668109)
75. Cruz, H.A., V.A. Brazhnyi, V.V. Konotop, and M. Salerno, 2009, " One-dimensional delocalizing transitions of matter waves in optical lattices, " Physica D (Amsterdam) 238, 1372. PDNPDT 0167-2789 10.1016/j.physd.2008. 09.008
76. Cuevas, J., B.A. Malomed, P.G. Kevrekidis, and D.J. Frantzeskakis, 2009, " Solitons in quasi-one-dimensional Bose-Einstein condensates with competing dipolar and local interactions, " Phys. Rev. A 79, 053608. PLRAAN 1050-2947 10.1103/PhysRevA.79.053608
77. Darmanyan, S., A. Kobyakov, and F. Lederer, 1998, " Strongly localized modes in discrete systems with quadratic nonlinearity, " Phys. Rev. E PLEEE8 1063-651X 57, 2344. 10.1103/PhysRevE.57.2344
78. Davies, E.B., 1979, " Symmetry breaking in a non-linear Schrödinger equation, " Commun. Math. Phys. CMPHAY 0010-3616 64, 191. 10.1007/BF01221731
79. Davis, K., K. Miura, N. Sugimoto, and K. Hirao, 1996, " Writing waveguides in glass with a fs-laser, " Opt. Lett. 21, 1729. OPLEDP 0146-9592 10.1364/OL.21.001729
80. Davis, K.B., M.-O. Mewes, M.R. Andrews, N.J. van Druten, D.S. Durfee, D.M. Kurn, and W. Ketterle, 1995, " Bose-Einstein condensation in a gas of sodium atoms, " Phys. Rev. Lett. 75, 3969. PRLTAO 0031-9007 10.1103/PhysRevLett.75.3969
81. De Nicola, S., B.A. Malomed, and R. Fedele, 2006, " An effective potential for one-dimensional matter-wave solitons in an axially inhomogeneous trap, " Phys. Lett. A 360, 164. PYLAAG 0375-9601 10.1016/j.physleta.2006. 07.062 (Pubitemid 44754735)
82. Desaix, M., D. Anderson, and M. Lisak, 1991, " Variational approach to collapse of optical pulses, " J. Opt. Soc. Am. B 8, 2082. JOBPDE 0740-3224 10.1364/JOSAB.8.002082
83. Dohnal, T., and D. Pelinovsky, 2008, " Surface gap solitons at a nonlinearity interface, " SIAM J. Appl. Dyn. Syst. 7, 249. SJADAY 1536-0040 10.1137/060676751
84. Dohnal, T., M. Plum, and W. Reichel, 2010, " Surface gap soliton ground states for the nonlinear Schrödinger equation, " arXiv:1011.2886v1.
85. Dong, G., B. Hu, and W. Lu, 2006, " Ground-state properties of a Bose-Einstein condensate tuned by a far-off-resonant optical field, " Phys. Rev. A 74, 063601. PLRAAN 1050-2947 10.1103/PhysRevA.74.063601 (Pubitemid 44866607)
86. Dong, L., and H. Li, 2010, " Surface solitons in nonlinear lattices, " J. Opt. Soc. Am. B 27, 1179. JOBPDE 0740-3224 10.1364/JOSAB.27.001179
87. Driben, R., and B.A. Malomed, 2008, " Stabilization of two-dimensional solitons and vortices against supercritical collapse by lattice potentials, " Eur. Phys. J. D 50, 317. EPJDF6 1434-6060 10.1140/epjd/e2008-00239-3
88. Driben, R., B.A. Malomed, A. Gubeskys, and J. Zyss, 2007, " Cubic-quintic solitons in the checkerboard potential, " Phys. Rev. E PLEEE8 1539-3755 76, 066604. 10.1103/PhysRevE.76.066604 (Pubitemid 350248352)
89. Dror, N., and B.A. Malomed, 2011, " Solitons supported by localized nonlinearities in periodic media, " Phys. Rev. A PLRAAN 1050-2947 83, 033828. 10.1103/PhysRevA.83.033828
90. Dudley, J.M., G. Genty, and S. Coen, 2006, " Supercontinuum generation in photonic crystal fiber, " Rev. Mod. Phys. 78, 1135. RMPHAT 0034-6861 10.1103/RevModPhys.78.1135 (Pubitemid 44521770)
91. Duree G.C., J.L. Shultz, G.J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E.J. Sharp, and R.R. Neurgaonkar, 1993, " Observation of self-trapping of an optical beam due to the photorefractive effect, " Phys. Rev. Lett. 71, 533. PRLTAO 0031-9007 10.1103/PhysRevLett.71.533
92. Dutta, O., A. Eckhardt, P. Hauke, B. Malomed, and M. Lewenstein, 2011, " Bose-Hubbard model with occupation-dependent parameters, " New J. Phys. NJOPFM 1367-2630 13, 023019. 10.1088/1367-2630/13/2/023019
93. Efremidis, N.K., J. Hudock, D.N. Christodoulides, J.W. Fleischer, O. Cohen, and M. Segev, 2003, " Two-dimensional optical lattice solitons, " Phys. Rev. Lett. 91, 213905. PRLTAO 0031-9007 10.1103/PhysRevLett.91. 213905
94. Efremidis, N.K., S. Sears, D.N. Christodoulides, J.W. Fleischer, and M. Segev, 2002, " Discrete solitons in photorefractive optically induced photonic lattices, " Phys. Rev. E PLEEE8 1063-651X 66, 046602. 10.1103/PhysRevE.66.046602 (Pubitemid 40606312)
95. Eggleton, B.J., C. Kerbage, P.S. Westbrook, R.S. Windeler, and A. Hale, 2001, " Microstructured optical fiber devices, " Opt. Express 9, 698. OPEXFF 1094-4087 10.1364/OE.9.000698
96. Eggleton, B.J., R.E. Slusher, C.M. de Sterke, P.A. Krug, and J.E. Sipe, 1996, " Bragg grating solitons, Phys. Rev. Lett. 76, 1627. PRLTAO 0031-9007 10.1103/PhysRevLett.76.1627
97. Eiermann, B.Th. Anker, M. Albiez, M. Taglieber, P. Treutlein, K.-P. Marzlin, and M.K. Oberthaler, 2004, " Bright Bose-Einstein gap solitons of atoms with repulsive interaction, " Phys. Rev. Lett. 92, 230401. PRLTAO 0031-9007 10.1103/PhysRevLett.92.230401
98. Eilbeck, J.C., P.S. Lomdahl, and A.C. Scott, 1985, " The discrete self-trapping equation, " Physica D (Amsterdam) 16, 318. PDNPDT 0167-2789 10.1016/0167-2789(85)90012-0
99. Eisenberg, H.S., Y. Silberberg, R. Morandotti, A.R. Boyd, and J.S. Aitchison, 1998, " Discrete spatial optical solitons in waveguide arrays, " Phys. Rev. Lett. PRLTAO 0031-9007 81, 3383. 10.1103/PhysRevLett.81.3383
100. El-Ganainy, R., S. Mokhov, K.G. Makris, D.N. Christodoulides, and R. Morandotti, 2006, " Solitons in dispersion-inverted AlGaAs nanowires, " Opt. Express OPEXFF 1094-4087 14, 2277. 10.1364/OE.14.002277
101. Etrich, C., F. Lederer, B.A. Malomed, T. Peschel, and U. Peschel, 2000, " Optical solitons in media with a quadratic nonlinearity, " Prog. Opt. 41, 483. POPTAN 0079-6638 10.1016/S0079-6638(00)80022-0
102. Fedichev, P.O., Y. Kagan, G.V. Shlyapnikov, and J.T.M. Walraven, 1996, " Influence of nearly resonant light on the scattering length in low-temperature atomic gases, " Phys. Rev. Lett. 77, 2913. PRLTAO 0031-9007 10.1103/PhysRevLett.77.2913
103. Ferrando, A., M. Zacares, P. Andrees, P. Fernandez de Cordoba, and J.A. Monsoriu, 2005 a, " Nodal solitons and the nonlinear breaking of discrete symmetry, " Opt. Express 13, 1072. OPEXFF 1094-4087 10.1364/OPEX.13.001072 (Pubitemid 40334832)
104. Ferrando, A., M. Zacares, P. Fernandez de Cordoba, D. Binosi, and J.A. Monsoriu, 2003, " Spatial soliton formation in photonic crystal fibers, " Opt. Express 11, 452. OPEXFF 1094-4087 10.1364/OE.11.000452
105. Ferrando, A., M. Zacares, P. Fernandez de Cordoba, D. Binosi, and J.A. Monsoriu, 2004, " Vortex solitons in photonic crystal fibers, " Opt. Express 12, 817. OPEXFF 1094-4087 10.1364/OPEX.12.000817
106. Ferrando, A., M. Zacares, and M.A. Garcia-March, 2005, " Vorticity cutoff in nonlinear photonic crystals, " Phys. Rev. Lett. 95, 043901. PRLTAO 0031-9007 10.1103/PhysRevLett.95.043901 (Pubitemid 41506210)
107. Ferrando, A., M. Zacares, M.A. Garcia-March, J.A. Monsoriu, and P. Fernandez de Cordoba, 2005 b, " Vortex transmutation, " Phys. Rev. Lett. 95, 123901. PRLTAO 0031-9007 10.1103/PhysRevLett.95.123901 (Pubitemid 41505618)
108. Fibich, G., Y. Sivan, and M.I. Weinstein, 2006, " Bound states of nonlinear Schrödinger equations with a periodic nonlinear microstructure, " Physica D (Amsterdam) 217, 31. PDNPDT 0167-2789 10.1016/j.physd.2006.03. 009 (Pubitemid 44304449)
109. Fischer, R., D. Träger, D.N. Neshev, A.A. Sukhorukov, W. Krolikowski, C. Denz, and Y.S. Kivshar, 2006, " Reduced-symmetry two-dimensional solitons in photonic lattices, " Phys. Rev. Lett. 96, 023905. PRLTAO 0031-9007 10.1103/PhysRevLett.96.023905 (Pubitemid 43248233)
110. Fleischer, J.W., G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D.N. Christodoulides, 2004, " Observation of vortex-ring 'discrete' solitons in 2D photonic lattices, " Phys. Rev. Lett. 92, 123904. PRLTAO 0031-9007 10.1103/PhysRevLett.92.123904
111. Fleischer, J.W., G. Bartal, O. Cohen, T. Schwartz, O. Manela, B. Freedman, M. Segev, H. Buljan, and N.K. Efremidis, 2005, " Spatial photonics in nonlinear waveguide arrays, " Opt. Express OPEXFF 1094-4087 13, 1780. 10.1364/OPEX.13.001780 (Pubitemid 40548737)
112. Fleischer, J.W., T. Carmon, M. Segev, N.K. Efremidis, and D.N. Christodoulides, 2003, " Observation of discrete solitons in optically induced real time waveguide arrays, " Phys. Rev. Lett. 90, 023902. PRLTAO 0031-9007 10.1103/PhysRevLett.90.023902
113. Fleischer, J.W., M. Segev, N.K. Efremidis, and D.N. Christodoulides, 2003, " Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices, " Nature (London) NATUAS 0028-0836 422, 147. 10.1038/nature01452 (Pubitemid 36362743)
114. Fratalocchi, A., G. Assanto, K.A. Brzdakiewicz, and M.A. Karpierz, 2004, " Discrete propagation and spatial solitons in nematic liquid crystals, " Opt. Lett. 29, 1530. OPLEDP 0146-9592 10.1364/OL.29.001530
115. Fuerbach, A., P. Steinvurzel, J.A. Bolger, A. Nulsen, and B.J. Eggleton, 2005, " Nonlinear propagation effects in antiresonant high-index inclusion photonic crystal fibers, " Opt. Lett. 30, 830. OPLEDP 0146-9592 10.1364/OL.30.000830 (Pubitemid 40567012)
116. Gallo, K., A. Pasquazi, S. Stivala, and G. Assanto, 2008, " Parametric solitons in two- dimensional lattices of purely nonlinear origin, " Phys. Rev. Lett. PRLTAO 0031-9007 100, 053901. 10.1103/PhysRevLett.100. 053901 (Pubitemid 351220711)
117. Garcia-March, M.A., A. Ferrando, M. Zacares, S. Sahu, and D.E. Ceballos-Herrera, 2009 b, " Symmetry, winding number, and topological charge of vortex solitons in discrete-symmetry media, " Phys. Rev. A 79, 053820. PLRAAN 1050-2947 10.1103/PhysRevA.79.053820
118. Garcia-March, M.A., A. Ferrando, M. Zacares, J. Vikande, and L.D. Carr, 2009 a, " Angular pseudomomentum theory for the generalized nonlinear Schrödinger equation in discrete rotational symmetry media, " Physica D (Amsterdam) 238, 1432. PDNPDT 0167-2789 10.1016/j.physd.2008.12.007
119. Garnier, J., and F.K. Abdullaev, 2006, " Transmission of matter-wave solitons through nonlinear traps and barriers, " Phys. Rev. A 74, 013604. PLRAAN 1050-2947 10.1103/PhysRevA.74.013604 (Pubitemid 44464318)
120. Ghanbari, S., T.D. Kieu, A. Sidorov, and P. Hannaford, 2006, " Permanent magnetic lattices for ultracold atoms and quantum degenerate gases, " J. Phys. B JPAPEH 0953-4075 39, 847. 10.1088/0953-4075/39/4/009
121. Gligorić, G., A. Maluckov, L. Hadzievski, and B.A. Malomed, 2008, " Bright solitons in the one-dimensional discrete Gross-Pitaevskii equation with dipole-dipole interactions, " Phys. Rev. A 78, 063615. PLRAAN 1050-2947 10.1103/PhysRevA.78.063615
122. Gligorić, G., A. Maluckov, L. Hadzievski, and B.A. Malomed, 2009, " Soliton stability and collapse in the discrete nonpolynomial Schrödinger equation with dipole-dipole interactions, " Phys. Rev. A 79, 053609. PLRAAN 1050-2947 10.1103/PhysRevA.79.053609
123. Gligorić, G., A. Maluckov, L. Salasnich, B.A. Malomed, and L. Hadzievski, 2009, " Two routes to the one-dimensional discrete nonpolynomial Schrödinger equation, " Chaos 19, 043105. CHAOEH 1054-1500 10.1063/1.3248269
124. Gligorić, G., A. Maluckov, M. Stepić, L. Hadzievski, and B.A. Malomed, 2010 a, " Two-dimensional discrete solitons in dipolar Bose-Einstein condensates, " Phys. Rev. A 81, 013633. PLRAAN 1050-2947 10.1103/PhysRevA.81.013633
125. Gligorić, G., A. Maluckov, M. Stepić, L. Hadzievski, and B.A. Malomed, 2010 b, " Discrete vortex solitons in dipolar Bose-Einstein condensates, " J. Phys. B JPAPEH 0953-4075 43, 055303. 10.1088/0953-4075/ 43/5/055303
126. Golam Ali, Sk., S.K. Roy, and B. Talukdar, 2010, " Stability of matter-wave solitons in optical lattice, " Eur. Phys. J. D 59, 269. EPJDF6 1434-6060 10.1140/epjd/e2010-00146-0
127. Gomez-Gardeñes, J., B.A. Malomed, L.M. FlorIa, and A.R. Bishop, 2006 b, " Discrete solitons and vortices in the two-dimensional Salerno model with competing nonlinearities, " Phys. Rev. E PLEEE8 1539-3755 74, 036607. 10.1103/PhysRevE.74.036607 (Pubitemid 44403691)
128. Gomez-Gardeñes, J., B.A. Malomed, L.M. FlorIa, and A.R. Bishop, 2006 a, " Solitons in the Salerno model with competing nonlinearities, " Phys. Rev. E PLEEE8 1539-3755 73, 036608. 10.1103/PhysRevE.73.036608
129. Goral, K., L. Santos, and M. Lewenstein, 2002, " Quantum phases of dipolar bosons in optical lattices, " Phys. Rev. Lett. 88, 170406. PRLTAO 0031-9007 10.1103/PhysRevLett.88.170406
130. Gorbach, A.V., and D.V. Skryabin, 2009, " Spatial solitons in periodic nanostructures, " Phys. Rev. A 79, 053812. PLRAAN 1050-2947 10.1103/PhysRevA.79.053812
131. Greiner, M., O. Mandel, T. Esslinger, T.W. Hansch, and I. Bloch, 2002, " Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms, " Nature (London) NATUAS 0028-0836 415, 39. 10.1038/415039a (Pubitemid 34062442)
132. Griesmaier, A., J. Werner, S. Hensler, J. Stuhler, and T. Pfau, 2005, " Bose-Einstein condensation of chromium, " Phys. Rev. Lett. 94, 160401. PRLTAO 0031-9007 10.1103/PhysRevLett.94.160401 (Pubitemid 40620281)
133. Gubeskys, A., B.A. Malomed, and I.M. Merhasin, 2005, " Alternate solitons: Nonlinearly managed one- and two-dimensional solitons in optical lattices, " Stud. Appl. Math. 115, 255. SAPMB6 0022-2526 10.1111/j.1467-9590.2005.00328.x (Pubitemid 41024669)
134. Guerin, W., J.-F. Riou, J.P. Gaebler, V. Josse, P. Bouyer, and A. Aspect, 2006, " Guided quasicontinuous atom laser, " Phys. Rev. Lett. 97, 200402. PRLTAO 0031-9007 10.1103/PhysRevLett.97.200402 (Pubitemid 44759877)
135. Hang, C., and V.V. Konotop, 2010, " All-optical steering of light via spatial Bloch oscillations in a gas of three-level atoms, " Phys. Rev. A 81, 053849. PLRAAN 1050-2947 10.1103/PhysRevA.81.053849
136. Hang, C., V.V. Konotop, and G. Huang, 2009, " Spatial solitons and instabilities of light beams in a three-level atomic medium with a standing-wave control field, " Phys. Rev. A 79, 033826. PLRAAN 1050-2947 10.1103/PhysRevA.79.033826
137. Hao, R., R. Yang, L. Li, and G. Zhou, 2008, " Solutions for the propagation of light in nonlinear optical media with spatially inhomogeneous nonlinearities, " Opt. Commun. 281, 1256. OPCOB8 0030-4018 10.1016/j.optcom.2007.10.093
138. Harrison, W.A., 1966, Pseudopotentials in the Theory of Metals (Benjamin, New York).
139. Hasegawa, A., and F. Tappert, 1973, " Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion, " Appl. Phys. Lett. 23, 142. APPLAB 0003-6951 10.1063/1.1654836
140. He, Y., D. Mihalache, and B. Hu, 2010, " Soliton drift, rebound, penetration, and trapping at the interface between media with uniform and spatially modulated nonlinearities, " Opt. Lett. 35, 1716. OPLEDP 0146-9592 10.1364/OL.35.001716
141. Henderson, K., C. Ryu, C. MacCormick, and M.G.I Boshier, 2009, " Experimental demonstration of painting arbitrary and dynamic potentials for Bose-Einstein condensates, " New J. Phys. 11, 043030. NJOPFM 1367-2630 10.1088/1367-2630/11/4/043030
142. Herrmann, J., U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J.C. Knight, W.J. Wadsworth, P.S.J. Russell, and G. Korn, 2002, " Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers, " Phys. Rev. Lett. 88, 173901. PRLTAO 0031-9007 10.1103/PhysRevLett.88.173901
143. Hizanidis, K., Y. Kominis, and N.K. Efremidis, 2008, " Interlaced linear-nonlinear optical waveguide arrays, " Opt. Express OPEXFF 1094-4087 16, 18296. 10.1364/OE.16.018296
144. Hukriede, J., D. Runde, and D. Kip, 2003, " Fabrication and application of holographic Bragg gratings in lithium niobate channel waveguides, " J. Phys. D JPAPBE 0022-3727 36, R1. 10.1088/0022-3727/36/3/201
145. Hung, N.V., P. Ziń, M. Trippenbach, and B.A. Malomed, 2010, " Two-dimensional solitons in media with the stripe-shaped nonlinearity modulation, " Phys. Rev. E PLEEE8 1539-3755 82, 046602. 10.1103/PhysRevE.82.046602
146. Ilan, B., and M.I. Weinstein, 2010, " Band-edge Solitons, Nonlinear Schrödinger/Gross-Pitaevskii Equations and Effective Media, " arXiv:1002.1986v2 [SIAM J. Multiscale Modeling and Simulation (to be published)].
147. Inouye, S., M.R. Andrews, J. Stenger, H.J. Miesner, D.M. Stamper-Kurn, and W. Ketterle, 1998, " Observation of Feshbach resonances in a Bose-Einstein condensate, " Nature (London) NATUAS 0028-0836 392, 151. 10.1038/32354 (Pubitemid 28162780)
148. Itoh, K., W. Watanabe, S. Nolte, and C.B. Schaffer, 2006, " Ultrafast processes for bulk modification of transparent materials, " MRS Bull. 31, 620. MRSBEA 0883-7694 10.1557/mrs2006.159
149. 3, " Ferroelectrics 50, 165. FEROA8 0015-0193 10.1080/00150198308014446
150. Jaksch D., C. Bruder, J.I. Cirac, C.W. Gardiner, and P. Zoller, 1998, " Cold bosonic atoms in optical lattices, " Phys. Rev. Lett. 81, 3108. PRLTAO 0031-9007 10.1103/PhysRevLett.81.3108
151. Jaksch, D., and P. Zoller, 2005, " The cold atom Hubbard toolbox, " Ann. Phys. (N.Y.) APNYA6 0003-4916 315, 52. 10.1016/j.aop.2004.09.010 (Pubitemid 40140154)
152. Joannopoulos, J.D., S.G. Johnson, J.N. Winn, and R.D. Meade, 2008, Photonic Crystals: Molding the Flow of Light (Princeton University Press, Princeton).
153. Johnson, S.G., S.H. Fan, P.R. Villeneuve, J.D. Joannopoulos, and L.A. Kolodzejski, 1999, " Guided modes in photonic crystal slabs, " Phys. Rev. B PRBMDO 0163-1829 60, 5751. 10.1103/PhysRevB.60.5751
154. Kanashov, A.A., and A.M. Rubenchik, 1981, " On diffraction and dispersion effects on three wave interaction, " Physica D (Amsterdam) 4, 122. PDNPDT 0167-2789 10.1016/0167-2789(81)90009-9
155. Kartashov, Y.V., A. Ferrando, A.A. Egorov, and L. Torner, 2005, " Soliton topology versus discrete symmetry in optical lattices, " Phys. Rev. Lett. 95, 123902. PRLTAO 0031-9007 10.1103/PhysRevLett.95.123902 (Pubitemid 41505619)
156. Kartashov, Y.V., B.A. Malomed, V.A. Vysloukh, and L. Torner, 2009 a, " Two-dimensional solitons in nonlinear lattices, " Opt. Lett. 34, 770. OPLEDP 0146-9592 10.1364/OL.34.000770
157. Kartashov, Y.V., B.A. Malomed, V.A. Vysloukh, and L. Torner, 2009 b, " Vector solitons in nonlinear lattices, " Opt. Lett. 34, 3625. OPLEDP 0146-9592 10.1364/OL.34.003625
158. Kartashov, Y.V., V.A. Vysloukh, A. Szameit, F. Dreisow, M. Heinrich, S. Nolte, A. Tünnermann, T. Pertsch, and L. Torner, 2008, " Surface solitons at interfaces of arrays with spatially modulated nonlinearity, " Opt. Lett. 33, 1120. OPLEDP 0146-9592 10.1364/OL.33.001120
159. Kartashov, Y.V., V.A. Vysloukh, and L. Torner, 2006, " Surface gap solitons, " Phys. Rev. Lett. 96, 073901. PRLTAO 0031-9007 10.1103/PhysRevLett.96.073901 (Pubitemid 43290817)
160. Kartashov, Y.V., V.A. Vysloukh, and L. Torner, 2008 a, " Propagation of solitons in thermal media with periodic nonlinearity, " Opt. Lett. 33, 1774. OPLEDP 0146-9592 10.1364/OL.33.001774
161. Kartashov, Y.V., V.A. Vysloukh, and L. Torner, 2008 b, " Soliton modes, stability, and drift in optical lattices with spatially modulated nonlinearity, " Opt. Lett. 33, 1747. OPLEDP 0146-9592 10.1364/OL.33.001747
162. Kartashov, Y.V., V.A. Vysloukh, and L. Torner, 2008 c, " Power-dependent shaping of vortex solitons in optical lattices with spatially modulated nonlinear refractive index, " Opt. Lett. 33, 2173. OPLEDP 0146-9592 10.1364/OL.33.002173
163. Kartashov, Y.V., V.A. Vysloukh, and L. Torner, 2009 a, " Soliton shape and mobility control in optical lattices, " Prog. Opt. 52, 63. POPTAN 0079-6638 10.1016/S0079-6638(08)00004-8
164. Kartashov, Y.V., V.A. Vysloukh, and L. Torner, 2009 b, " Multipole surface solitons in thermal media, " Opt. Lett. 34, 283. OPLEDP 0146-9592 10.1364/OL.34.000283
165. Kartashov, Y.V., F. Ye, V.A. Vysloukh, and L. Torner, 2007, " Surface waves in defocusing thermal media, " Opt. Lett. 32, 2260. OPLEDP 0146-9592 10.1364/OL.32.002260 (Pubitemid 351299503)
166. Kartashov, Y.V., A.S. Zelenina, L. Torner, and V.A. Vysloukh, 2004, " Spatial soliton switching in quasi-continuous optical arrays, " Opt. Lett. 29, 766. OPLEDP 0146-9592 10.1364/OL.29.000766
167. Kevrekidis, P.G., 2009, Ed., Discrete Nonlinear Schrödinger Equation: Mathematical Analysis, Numerical Computations and Physical Perspectives (Springer, Berlin).
168. Kevrekidis, P.G., D.J. Frantzeskakis, and R. Carretero-González, 2008, Eds., Emergent Nonlinear Phenomena in Bose-Einstein Condensates (Springer, Berlin).
169. Kevrekidis, P.G., K.Ø. Rasmussen, and A.R. Bishop, 2001, " The discrete nonlinear Schrodinger equation: A survey of recent results, " Int. J. Mod. Phys. B IJPBEV 0217-9792 15, 2833. 10.1142/S0217979201007105
170. Khaykovich, L., F. Schreck, G. Ferrari, T. Bourdel, J. Cubizolles, L.D. Carr, Y. Castin, and C. Salomon, 2002, " Formation of a matter-wave bright soliton, " Science 296, 1290. SCIEAS 0036-8075 10.1126/science.1071021 (Pubitemid 34522779)
171. Kivshar, Y.S., and G.P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic Press, San Diego, 2003).
172. Kivshar, Y.S., Z. Fei, and L. Vázquez, 1991, " Resonant soliton-impurity interactions, " Phys. Rev. Lett. 67, 1177. PRLTAO 0031-9007 10.1103/PhysRevLett.67.1177
173. Kivshar, Y.S., and B.A. Malomed, 1989, " Dynamics of solitons in nearly integrable systems, " Rev. Mod. Phys. 61, 763. RMPHAT 0034-6861 10.1103/RevModPhys.61.763
174. Knight, J.C., T.A. Birks, P.S. Russell, and D.M. Atkin, 1996, " All-silica single-mode optical fiber with photonic crystal cladding, " Opt. Lett. 21, 1547. OPLEDP 0146-9592 10.1364/OL.21.001547
175. Kominis, Y., and T. Bountis, 2010, " Analytical solutions of systems with piecewise linear dynamics, " Int. J. Bifurcation Chaos 20, 509 10.1142/S0218127410025570.
176. Kominis, Y., 2006, " Analytical solitary wave solutions of the nonlinear Kronig-Penney model in photonic structures, " Phys. Rev. E PLEEE8 1539-3755 73, 066619. 10.1103/PhysRevE.73.066619 (Pubitemid 43937645)
177. Kominis, Y., and K. Hizanidis, 2006, " Lattice solitons in self-defocusing optical media: Analytical solutions of the nonlinear Kronig-Penney model, " Opt. Lett. 31, 2888. OPLEDP 0146-9592 10.1364/OL.31.002888 (Pubitemid 44604044)
178. Kominis, Y., and K. Hizanidis, 2008, " Power dependent soliton location and stability in complex photonic structures, " Opt. Express 16, 12124. OPEXFF 1094-4087 10.1364/OE.16.012124
179. Kominis, Y., A. Papadopoulos, and K. Hizanidis, 2007, " Surface solitons in waveguide arrays: Analytical solutions, " Opt. Express 15, 10041. OPEXFF 1094-4087 10.1364/OE.15.010041 (Pubitemid 47230822)
180. Krauss, T.F., R.M. DeLaRue, and S. Brand, 1996, " Two-dimensional photonic-bandgap structures operating at near infrared wavelengths, " Nature (London) NATUAS 0028-0836 383, 699. 10.1038/383699a0 (Pubitemid 26360641)
181. Lahaye, T., C. Menotti, L. Santos, M. Lewenstein, and T. Pfau, 2009, Rep. Prog. Phys. RPPHAG 0034-4885 72, 126401. 10.1088/0034-4885/72/12/126401
182. Larsen, T.T., A. Bjarklev, D.S. Hermann, and J. Broeng, 2003, " Optical devices based on liquid crystal photonic bandgap fibers, " Opt. Express 11, 2589. OPEXFF 1094-4087 10.1364/OE.11.002589
183. Leblond, H., B.A. Malomed, and D. Mihalache, 2009, " Stable vortex solitons in the Ginzburg-Landau model of a two-dimensional lasing medium with a transverse grating, " Phys. Rev. A 80, 033835. PLRAAN 1050-2947 10.1103/PhysRevA.80.033835
184. Lederer, F., G.I. Stegeman, D.N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, 2008, " Discrete solitons in optics, " Phys. Rep. 463, 1. PRPLCM 0370-1573 10.1016/j.physrep.2008.04.004
185. Lewenstein M., A. Sanpera, V. Ahufinger, B. Damski, A. De Sen, and U. Sen, 2007, " Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond, " Adv. Phys. 56, 243. ADPHAH 0001-8732 10.1080/00018730701223200 (Pubitemid 46710973)
186. Li, Z.D., P.B. He, L. Li, J.Q. Liang, and W.M. Liu, 2005, " Magnetic soliton and soliton collisions of spinor Bose-Einstein condensates in an optical lattice, " Phys. Rev. A 71, 053611. PLRAAN 1050-2947 10.1103/PhysRevA.71.053611 (Pubitemid 41481299)
187. Lin, T.-C., J. Wei, and W. Yao, 2010, " Orbital stability of bound states of nonlinear Schrodinger equations with linear and nonlinear optical lattices, " J. Diff. Equ. JDEQAK 0022-0396 (in press).
188. Liu, X., L.J. Qian, and F.W. Wise, 1999, " Generation of optical spatiotemporal solitons, " Phys. Rev. Lett. 82, 4631. PRLTAO 0031-9007 10.1103/PhysRevLett.82.4631
189. Liu, Y., G. Bartal, D.A. Genov, and X. Zhang, 2007, " Subwavelength discrete solitons in nonlinear metamaterials, " Phys. Rev. Lett. 99, 153901. PRLTAO 0031-9007 10.1103/PhysRevLett.99.153901 (Pubitemid 47569117)
190. Luan, F., A.K. George, T.D. Hedeley, G.J. Pearce, D.M. Bird, J.C. Knight, and P.S.J. Russell, 2004, " All-solid photonic bandgap fiber, " Opt. Lett. 29, 2369. OPLEDP 0146-9592 10.1364/OL.29.002369
191. Machacek, D.L., E.A. Foreman, Q.E. Hoq, P.G. Kevrekidis, A. Saxena, D.J. Frantzeskakis, and A.R. Bishop, 2006, " Statics and dynamics of an inhomogeneously nonlinear lattice, " Phys. Rev. E PLEEE8 1539-3755 74, 036602. 10.1103/PhysRevE.74.036602 (Pubitemid 44343486)
192. Maes, B., P. Bienstman, and R. Baets, 2005, " Bloch modes and self-localized waveguides in nonlinear photonic crystals, " J. Opt. Soc. Am. B 22, 613. JOBPDE 0740-3224 10.1364/JOSAB.22.000613 (Pubitemid 40555801)
193. Makris, K.G., S. Suntsov, D.N. Christodoulides, G.I. Stegeman, and A. Hache, 2005, " Discrete surface solitons, " Opt. Lett. 30, 2466. OPLEDP 0146-9592 10.1364/OL.30.002466 (Pubitemid 41463522)
194. Malomed, B.A., 2006, Soliton Management in Periodic Systems (Springer, New York).
195. Malomed, B.A., and M.Y. Azbel, 1993, " Modulational instability of a wave scattered by a nonlinear center, " Phys. Rev. B PRBMDO 0163-1829 47, 10402. 10.1103/PhysRevB.47.10402
196. Malomed, B.A., D. Mihalache, F. Wise, and L. Torner, 2005, " Spatiotemporal optical solitons, " J. Opt. B 7, R53. JOBOFD 1464-4266 10.1088/1464-4266/7/5/R02 (Pubitemid 40665898)
197. Malomed, B.A., and M.I. Weinstein, 1996, " Soliton dynamics in the discrete nonlinear Schrödinger equation, " Phys. Lett. A 220, 91. PYLAAG 0375-9601 10.1016/0375-9601(96)00516-6
198. Maluckov, A., Lj. Hadzievski, B.A. Malomed, and L. Salasnich, 2008, " Solitons in the discrete nonpolynomial Schrödinger equation, " Phys. Rev. A 78, 013616. PLRAAN 1050-2947 10.1103/PhysRevA.78.013616
199. Maneuf, S., R. Desailly, and C. Froehly, 1988, " Stable self-trapping of laser beams: Observation in a nonlinear planar waveguides, " Opt. Commun. 65, 193. OPCOB8 0030-4018 10.1016/0030-4018(88)90348-3 (Pubitemid 18565648)
200. Maneuf, S., and F. Reynaud, 1988, " Quasi-steady state self-trapping of first, second, and third order subnanosecond soliton beams, " Opt. Commun. 66, 325. OPCOB8 0030-4018 10.1016/0030-4018(88)90424-5 (Pubitemid 18625425)
201. Marinescu, M., and L. You, 1998, " Controlling atom-atom interaction at ultralow temperature by dc electric field, " Phys. Rev. Lett. 81, 4596. PRLTAO 0031-9007 10.1103/PhysRevLett.81.4596
202. Marini, A., A.V. Gorbach, and D.V. Skryabin, 2010, " Coupled mode approach to surface plasmon polaritons in nonlinear periodic structures, " Opt. Lett. 35, 3532. OPLEDP 0146-9592 10.1364/OL.35.003532
203. Martin, H., E.D. Eugenieva, Z. Chen, and D.N. Christodoulides, 2004, " Discrete solitons and soliton-induced dislocations in partially coherent photonic lattices, " Phys. Rev. Lett. 92, 123902. PRLTAO 0031-9007 10.1103/PhysRevLett.92.123902
204. Mayteevarunyoo, T., and B.A. Malomed, 2008, " Solitons in one-dimensional photonic crystals, " J. Opt. Soc. Am. B 25, 1854. JOBPDE 0740-3224 10.1364/JOSAB.25.001854
205. Mayteevarunyoo, T., B.A. Malomed, and G. Dong, 2008, " Spontaneous symmetry breaking in a nonlinear double-well structure, " Phys. Rev. A 78, 053601. PLRAAN 1050-2947 10.1103/PhysRevA.78.053601
206. Mihalache, D., D. Mazilu, F. Lederer, B.A. Malomed, L.-C. Crasovan, Y.V. Kartashov, and L. Torner, 2005, " Stable three-dimensional solitons in attractive Bose-Einstein condensates loaded in an optical lattice, " Phys. Rev. A 72, 021601(R). PLRAAN 1050-2947 10.1103/PhysRevA.72.021601 (Pubitemid 43272638)
207. Milburn, C.J., J. Corney, E.M. Wright, and D.W. Walls, 1997, " Quantum dynamics of an atomic Bose-Einstein condensate in a double-well potential, " Phys. Rev. A 55, 4318. PLRAAN 1050-2947 10.1103/PhysRevA.55. 4318
208. Minardi, S., F. Eilenberger, Y.V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, 2010, " Three-dimensional light bullets in arrays of waveguides, " Phys. Rev. Lett. PRLTAO 0031-9007 105, 263901. 10.1103/PhysRevLett.105.263901
209. Mingaleev, S.F., and Y.S. Kivshar, 2001, " Self-trapping and stable localized modes in nonlinear photonic crystals, " Phys. Rev. Lett. 86, 5474. PRLTAO 0031-9007 10.1103/PhysRevLett.86.5474 (Pubitemid 32548944)
210. Mollenauer, L.F., R.H. Stolen, and J.P. Gordon, 1980, " Experimental observation of picosecond pulse narrowing and solitons in optical fibers, " Phys. Rev. Lett. 45, 1095. PRLTAO 0031-9007 10.1103/PhysRevLett.45.1095
211. Morsch, O., J.H. Muller, M. Cristiani, D. Ciampini, and E. Arimondo, 2001, " Bloch oscillations and mean-field effects of Bose-Einstein condensates in one-dimensional optical lattices, " Phys. Rev. Lett. 87, 140402. PRLTAO 0031-9007 10.1103/PhysRevLett.87.140402 (Pubitemid 32962123)
212. Morsch, O., and M. Oberthaler, 2006, " Dynamics of Bose-Einstein condensates in optical lattices, " Rev. Mod. Phys. 78, 179. RMPHAT 0034-6861 10.1103/RevModPhys.78.179
213. Muñoz Mateo, A., and V. Delgado, 2008, " Effective mean-field equations for cigar-shaped and disk-shaped Bose-Einstein condensates, " Phys. Rev. A 77, 013617. PLRAAN 1050-2947 10.1103/PhysRevA.77.013617 (Pubitemid 351161682)
214. Neshev, D., T.J. Alexander, E.A. Ostrovskaya, Y.S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, 2004, " Observation of discrete vortex solitons in optically induced photonic lattices, " Phys. Rev. Lett. 92, 123903. PRLTAO 0031-9007 10.1103/PhysRevLett.92.123903
215. Neshev, D., E.A. Ostrovskaya, Y. Kivshar, and W. Krolikowski, 2003, " Spatial solitons in optically induced gratings, " Opt. Lett. 28, 710. OPLEDP 0146-9592 10.1364/OL.28.000710
216. Niarchou, P., G. Theocharis, P.G. Kevrekidis, P. Schmelcher, and D.J. Frantzeskakis, 2007, " Soliton oscillations in collisionally inhomogeneous attractive Bose-Einstein condensates, " Phys. Rev. A 76, 023615. PLRAAN 1050-2947 10.1103/PhysRevA.76.023615 (Pubitemid 47357766)
217. Noda, S., K. Tomoda, N. Yamamoto, and A. Chutinan, 2000, " Full three-dimensional photonic bandgap crystals at near-infrared wavelengths, " Science 289, 604. SCIEAS 0036-8075 10.1126/science.289.5479.604 (Pubitemid 30622060)
218. Öster, M., and M. Johansson, 2005, Phase twisted modes and current reversals in a lattice model of waveguide arrays with nonlinear coupling, " Phys. Rev. E PLEEE8 1539-3755 71, 025601(R). 10.1103/PhysRevE.71.025601 (Pubitemid 40607013)
219. Öster, M., and M. Johansson, 2009, " Stability, mobility and power currents in a two-dimensional model for waveguide array with nonlinear coupling, " Physica D (Amsterdam) 238, 88. PDNPDT 0167-2789 10.1016/j.physd.2008.08.006
220. Öster, M., M. Johansson, and A. Eriksson, 2003, " Enhanced mobility of strongly localized modes in waveguide arrays by inversion of stability, " Phys. Rev. E PLEEE8 1063-651X 67, 056606. 10.1103/PhysRevE.67. 056606
221. Ouzounov, D.G., F.R. Ahmad, D. Muller, N. Venkataraman, M.T. Gallagher, M. G. Thomas, J. Silcox, K.W. Koch, and A.L. Gaeta, 2003, " Generation of megawatt optical solitons in hollow-core photonic band-gap fibers, " Science SCIEAS 0036-8075 301, 1702 10.1126/science.1088387.
222. Panoiu, N.C., B.A. Malomed, and R.M. Osgood, 2008, " Semidiscrete solitons in arrayed waveguide structures with Kerr nonlinearity, " Phys. Rev. A 78, 013603. PLRAAN 1050-2947 10.1103/PhysRevA.78.013603
223. Panoiu, N.C., R.M. Osgood, and B.A. Malomed, 2006, " Semidiscrete composite solitons in arrays of quadratically nonlinear waveguides, " Opt. Lett. 31, 1097. OPLEDP 0146-9592 10.1364/OL.31.001097 (Pubitemid 43837464)
224. Paredes, B., A. Widera, V. Murg, O. Mandel, S. Fölling, I. Cirac, G.V. Shlyapnikov, T.W. Hansch, and I. Bloch, 2004, " Tonks-Girardeau gas of ultracold atoms in an optical lattice, " Nature (London) NATUAS 0028-0836 429, 277. 10.1038/nature02530 (Pubitemid 38684809)
225. Pasquazi, A., and G. Assanto, 2009, " Quadratic solitons in degenerate quasi-phase-matched noncollinear geometry, " Phys. Rev. A 80, 021801(R). PLRAAN 1050-2947 10.1103/PhysRevA.80.021801
226. Peccianti, M., G. Assanto, A. Dyadyusha, and M. Kaczmarek, 2007, " Nonlinear shift of spatial solitons at a graded dielectric interface, " Opt. Lett. 32, 271. OPLEDP 0146-9592 10.1364/OL.32.000271 (Pubitemid 46339967)
227. Peccianti, M., C. Conti, and G. Assanto, 2005, " Interplay between nonlocality and nonlinearity in nematic liquid crystals, " Opt. Lett. 30, 415. OPLEDP 0146-9592 10.1364/OL.30.000415 (Pubitemid 40297439)
228. Peccianti, M., C. Conti, G. Assanto, A. de Luca, and C. Umeton, 2004, " Routing of anisotropic spatial solitons and modulational instability in liquid crystals, " Nature (London) NATUAS 0028-0836 432, 733. 10.1038/nature03101 (Pubitemid 39662719)
229. Peccianti, M., A. Dyadyusha, M. Kaczmarek, and G. Assanto, 2006, " Tunable refraction and reflection of self-confined light beams, " Nature Phys. 2, 737. NPAHAX 1745-2473 10.1038/nphys427 (Pubitemid 44691278)
230. Perez-Garcia, V.M., and R. Pardo, 2009, " Localization phenomena in nonlinear Schrödinger equations with spatially inhomogeneous nonlinearities: Theory and applications to Bose-Einstein condensates, " Physica D (Amsterdam) 238, 1352. PDNPDT 0167-2789 10.1016/j.physd.2008.08.020
231. Peschel, T., U. Peschel, and F. Lederer, 1998, " Discrete bright solitary waves in quadratically nonlinear media, " Phys. Rev. E PLEEE8 1063-651X 57, 1127. 10.1103/PhysRevE.57.1127
232. Pitaevskii, L.P., and A. Stringari, 2003, Bose-Einstein Condensation (Clarendon Press, Oxford).
233. Porter, M.A., P.G. Kevrekidis, B.A. Malomed, and D.J. Frantzeskakis, 2007, " Modulated amplitude waves in collisionally inhomogeneous Bose-Einstein condensates, " Physica D (Amsterdam) 229, 104. PDNPDT 0167-2789 10.1016/j.physd.2007.02.012 (Pubitemid 46778871)
234. Primatarowa, M.T., K.T. Stoychev, and R.S. Kamburova, 2005, " Interaction of solitons with extended nonlinear defects, " Phys. Rev. E PLEEE8 1539-3755 72, 036608. 10.1103/PhysRevE.72.036608 (Pubitemid 41778221)
235. Pushkarov, K.I., D.I. Pushkarov, and I.V. Tomov, 1979, " Self-action of light beams in nonlinear media: Soliton solutions, " Opt. Quantum Electron. OQELDI 0306-8919 11, 471. 10.1007/BF00620372
236. Qian, L.C., M.L. Wall, S. Zhan, Z. Zhou, and H. Pu, 2008, " Bose-Einstein condensates in a ring with periodic scattering length, " Phys. Rev. A PLRAAN 1050-2947 77, 013611. 10.1103/PhysRevA.77.013611
237. Raghavan, S., A. Smerzi, S. Fantoni, and S. Shenoy, 1999, " Coherent oscillations between two weakly coupled Bose-Einstein condensates: Josephson effects, π oscillations, and macroscopic quantum self-trapping, " Phys. Rev. A 59, 620. PLRAAN 1050-2947 10.1103/PhysRevA.59.620
238. Rajendran, S., P. Muruganandam, and M. Lakshmanan, 2010, " Bright and dark solitons in a quasi-1D Bose-Einstein condensates modelled by 1D Gross-Pitaevskii equation with time-dependent parameters, " Physica D (Amsterdam) 239, 366. PDNPDT 0167-2789 10.1016/j.physd.2009.12.005
239. Ranka, J.K., R.S. Windeler, and A.J. Stentz, 2000, " Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm, " Opt. Lett. 25, 25. OPLEDP 0146-9592 10.1364/OL.25.000025
240. Rapti, Z., P.G. Kevrekidis, V.V. Konotop, and C.K.R.T. Jones, 2007, " Solitary waves under the competition of linear and nonlinear periodic potentials, " J. Phys. A 1751-8113 40, 14151. 10.1088/1751-8113/40/47/008
241. Rasmussen, P.D., F.H. Bennet, D.N. Neshev, A.A. Sukhorukov, C.R. Rosberg, W. Krolikowski, O. Bang, and Y.S. Kivshar, 2009, " Observation of two-dimensional nonlocal gap solitons, " Opt. Lett. 34, 295. OPLEDP 0146-9592 10.1364/OL.34.000295
242. Reeves, N.H., D.V. Skryabin, F. Biancalana, J.C. Knight, P.S. Russell, F.G. Omenetto, A. Efimov, and A.J. Taylor, 2003, " Transformation and control of ultra-short pulses in dispersion-engineered photonic crystal fibers. " Nature (London) NATUAS 0028-0836 424, 511 10.1038/nature01798.
243. Robins, N.P., C. Figl, M. Jeppesen, G.R. Dennis, and J.D. Close, 2008, " A pumped atom laser, " Nature Phys. 4, 731. NPAHAX 1745-2473 10.1038/nphys1027
244. Rodas-Verde, M.I., H. Michinel, and V.M. Pérez-García., 2005, " Controllable soliton emission from a Bose-Einstein condensate, " Phys. Rev. Lett. 95, 153903. PRLTAO 0031-9007 10.1103/PhysRevLett.95. 153903 (Pubitemid 41777508)
245. Rodrigues, A.S., P.G. Kevrekidis, M.A. Porter, D.J. Frantzeskakis, P. Schmelcher, and A.R. Bishop, 2008, " Matter-wave solitons with a periodic, piecewise-constant scattering length, " Phys. Rev. A 78, 013611. PLRAAN 1050-2947 10.1103/PhysRevA.78.013611
246. Rosberg, C.R., F.H. Bennet, D.N. Neshev, P.D. Rasmussen, O. Bang, W. Krolikowski, A. Bjarklev, and Y.S. Kivshar, 2007, " Tunable diffraction and self-defocusing in liquid-filled photonic crystal fibers, " Opt. Express 15, 12145. OPEXFF 1094-4087 10.1364/OE.15.012145 (Pubitemid 47460078)
247. Rosberg, C.R., D.N. Neshev, W. Krolikowski, A. Mitchell, R.A. Vicencio, M.I. Molina, and Y.S. Kivshar, 2006, " Observation of surface gap solitons in semi-infinite waveguide arrays, " Phys. Rev. Lett. 97, 083901. PRLTAO 0031-9007 10.1103/PhysRevLett.97.083901 (Pubitemid 44277567)
248. Rotschild, C., B. Alfassi, O. Cohen, and M. Segev, 2006 a, " Long-range interactions between optical solitons, " Nature Phys. 2, 769. NPAHAX 1745-2473 10.1038/nphys445 (Pubitemid 44691284)
249. Rotschild, C., O. Cohen, O. Manela, M. Segev, and T. Carmon, 2005, " Solitons in nonlinear media with an infinite range of nonlocality: first observation of coherent elliptic solitons and of vortex-ring solitons, " Phys. Rev. Lett. 95, 213904. PRLTAO 0031-9007 10.1103/PhysRevLett.95.213904 (Pubitemid 41777047)
250. Rotschild, C., M. Segev, Z. Xu, Y.V. Kartashov, L. Torner, and O. Cohen, 2006 b, " Two-dimensional multipole solitons in nonlocal nonlinear media, " Opt. Lett. 31, 3312. OPLEDP 0146-9592 10.1364/OL.31.003312 (Pubitemid 44925380)
251. Russell, P. St. J., 2003, " Photonic crystal fibers, " Science 299, 358. SCIEAS 0036-8075 10.1126/science.1079280 (Pubitemid 36120031)
252. Sakaguchi, H., and B.A. Malomed, 2004 a, " Resonant nonlinearity management for nonlinear Schrödinger solitons, " Phys. Rev. E PLEEE8 1539-3755 70, 066613. 10.1103/PhysRevE.70.066613 (Pubitemid 40429876)
253. Sakaguchi, H., and B.A. Malomed, 2004 b, " Dynamics of positive- and negative-mass solitons in optical lattices and inverted traps, " J. Phys. B JPAPEH 0953-4075 37, 1443. 10.1088/0953-4075/37/7/006
254. Sakaguchi, H., and B.A. Malomed, 2004 c, " Two-dimensional loosely and tightly bound solitons in optical lattices and inverted traps, " J. Phys. B JPAPEH 0953-4075 37, 2225. 10.1088/0953-4075/37/11/001
255. Sakaguchi, H., and B.A. Malomed, 2005 a, " Matter-wave solitons in nonlinear optical lattices, " Phys. Rev. E PLEEE8 1539-3755 72, 046610. 10.1103/PhysRevE.72.046610 (Pubitemid 41778005)
256. Sakaguchi, H., and B.A. Malomed, 2005 b, " Higher-order vortex solitons, multipoles, and supervortices on a square optical lattice, " Europhys. Lett. 72, 698. EULEEJ 0295-5075 10.1209/epl/i2005-10295-7 (Pubitemid 41760387)
257. Sakaguchi, H., and B.A. Malomed, 2006 a, " Two-dimensional solitons in the Gross-Pitaevskii equation with spatially modulated nonlinearity, " Phys. Rev. E PLEEE8 1539-3755 73, 026601. 10.1103/PhysRevE.73.026601 (Pubitemid 43287676)
258. Sakaguchi, H., and B.A. Malomed, 2006 b, " Gap solitons in quasiperiodic optical lattices, " Phys. Rev. E PLEEE8 1539-3755 74, 026601. 10.1103/PhysRevE.74.026601 (Pubitemid 44200593)
259. Sakaguchi, H., and B.A. Malomed, 2007, " Channel-guided light bullets, " Phys. Rev. A 75, 063825. PLRAAN 1050-2947 10.1103/PhysRevA.75. 063825 (Pubitemid 47139442)
260. Sakaguchi, H., and B.A. Malomed, 2010, " Solitons in combined linear and nonlinear lattice potentials, " Phys. Rev. A 81, 013624. PLRAAN 1050-2947 10.1103/PhysRevA.81.013624
261. Salasnich, L., A. Cetoli, B.A. Malomed, and F. Toigo, 2007 a, " Nearly-one-dimensional self-attractive Bose-Einstein condensates in optical lattices, " Phys. Rev. A 75, 033622. PLRAAN 1050-2947 10.1103/PhysRevA.75. 033622 (Pubitemid 46515768)
262. Salasnich, L., and B.A. Malomed, 2009, " Solitons and solitary vortices in pancake-shaped Bose-Einstein condensates, " Phys. Rev. A 79, 053620. PLRAAN 1050-2947 10.1103/PhysRevA.79.053620
263. Salasnich, L., B.A. Malomed, and F. Toigo, 2007, " Matter-wave vortices in cigar-shaped and toroidal waveguides, " Phys. Rev. A 76, 063614. PLRAAN 1050-2947 10.1103/PhysRevA.76.063614 (Pubitemid 350281248)
264. Salasnich, L., A. Parola, and L. Reatto, 2002, " Effective wave equations for the dynamics of cigar-shaped and disk-shaped Bose condensates, " Phys. Rev. A 65, 043614. PLRAAN 1050-2947 10.1103/PhysRevA.65.043614
265. Salasnich, L, A. Cetoli, B.A. Malomed, F. Toigo, and L. Reatto, 2007, " Bose-Einstein condensates under a spatially-modulated transverse confinement, " Phys. Rev. A 76, 013623. PLRAAN 1050-2947 10.1103/PhysRevA.76.013623 (Pubitemid 47169142)
266. Salerno, M., 1992, " Quantum deformations of the discrete nonlinear Schrödinger equation, " Phys. Rev. A 46, 6856. PLRAAN 1050-2947 10.1103/PhysRevA.46.6856
267. Salerno, M., V.V. Konotop, and Y.V. Bludov, 2008, " Long-living Bloch oscillations of matter waves in periodic potentials, " Phys. Rev. Lett. 101, 030405. PRLTAO 0031-9007 10.1103/PhysRevLett.101.030405
268. Salgueiro, J.R., and Y.S. Kivshar, 2005, " Nonlinear dual-core photonic crystal fiber couplers, " Opt. Lett. 30, 1858. OPLEDP 0146-9592 10.1364/OL.30.001858
269. Salgueiro, J.R., and Y.S. Kivshar, 2009, " Optical vortex solitons and soliton clusters in photonic crystal fibers, " Eur. Phys. J. Special Topics 173, 281. 1951-6355 10.1140/epjst/e2009-01080-0
270. Salgueiro, J.R., Y.S. Kivshar, D.E. Pelinovsky, V. Simon, and H. Michinel, 2005, " Spatial vector solitons in nonlinear photonic crystal fibers, " Stud. Appl. Math. 115, 157. SAPMB6 0022-2526 10.1111/j.1467-9590. 2005.00324.x (Pubitemid 41018254)
271. Salgueiro, J.R., and F. Santos, 2009, " Nonlinear vortex modes in dual-core photonic crystal fiber couplers, " J. Opt. Soc. Am. B 26, 2301. JOBPDE 0740-3224 10.1364/JOSAB.26.002301
272. 3, " Appl. Phys. Lett. 25, 458. APPLAB 0003-6951 10.1063/1.1655547
273. Serkin, V.N., and A. Hasegawa, 2000, " Novel soliton solutions of the nonlinear Schrödinger equation model, " Phys. Rev. Lett. 85, 4502. PRLTAO 0031-9007 10.1103/PhysRevLett.85.4502 (Pubitemid 32024876)
274. Serkin, V.N., and A. Hasegawa, 2002, " Exactly integrable nonlinear Schrödinger equation models with varying dispersion, nonlinearity and gain: Application for soliton dispersion managements, " IEEE J. Sel. Top. Quantum Electron. IJSQEN 1077-260X 8, 418. 10.1109/JSTQE.2002.1016344 (Pubitemid 34854328)
275. Serkin, V.N., A. Hasegawa, and T.L. Belyaeva, 2007, " Nonatonomous solitons in external potentials, " Phys. Rev. Lett. 98, 074102. PRLTAO 0031-9007 10.1103/PhysRevLett.98.074102
276. Serkin, V.N., A. Hasegawa, and T.L. Belyaeva, 2010, " Nonatonomous matter-wave solitons near the Feshbach resonance, " Phys. Rev. A 81, 023610. PLRAAN 1050-2947 10.1103/PhysRevA.81.023610
277. Shi, Z., and J. Yang, 2007, " Solitary waves bifurcated from Bloch-band edges in two-dimensional periodic media, " Phys. Rev. E PLEEE8 1539-3755 75, 056602. 10.1103/PhysRevE.75.056602 (Pubitemid 46707810)
278. Silberberg, Y., 1990, " Collapse of optical pulses, " Opt. Lett. 15, 1282. OPLEDP 0146-9592 10.1364/OL.15.001282
279. Sivan, Y., G. Fibich, B. Ilan, and M.I. Weinstein, 2008, " Qualitative and quantitative analysis of stability and instability dynamics of positive lattice solitons, " Phys. Rev. E PLEEE8 1539-3755 78, 046602. 10.1103/PhysRevE.78.046602
280. Sivan, Y., G. Fibich, and M.I. Weinstein, 2006, " Waves in nonlinear lattices: Ultrashort optical pulses and Bose-Einstein condensates, " Phys. Rev. Lett. 97, 193902. PRLTAO 0031-9007 10.1103/PhysRevLett.97.193902 (Pubitemid 44730143)
281. Skarka, V., and N.B. Aleksic, 2006, " Stability criterion for dissipative soliton solutions of the one-, two-, and three-dimensional complex cubic-quintic Ginzburg-Landau equations, " Phys. Rev. Lett. 96, 013903. PRLTAO 0031-9007 10.1103/PhysRevLett.96.013903 (Pubitemid 43248348)
282. Skryabin, D.V., and A.V. Gorbach, 2010, " Colloquium: Looking at a soliton through the prism of optical supercontinuum, " Rev. Mod. Phys. 82, 1287. RMPHAT 0034-6861 10.1103/RevModPhys.82.1287
283. Smerzi, A., S. Fantoni, S. Giovanazzi, and S.R. Shenoy, 1997, " Quantum Coherent Atomic Tunneling between Two Trapped Bose-Einstein Condensates, " Phys. Rev. Lett. 79, 4950. PRLTAO 0031-9007 10.1103/PhysRevLett.79.4950
284. Smerzi, A., and A. Trombettoni, 2003, " Nonlinear tight-binding approximation for Bose-Einstein condensates in a lattice, " Phys. Rev. A 68, 023613. PLRAAN 1050-2947 10.1103/PhysRevA.68.023613
285. Smirnov, E., M. Stepic, C.E. Rüter, D. Kip, and V. Shandarov, 2006, " Observation of staggered surface solitary waves in one-dimensional waveguide arrays, " Opt. Lett. 31, 2338. OPLEDP 0146-9592 10.1364/OL.31.002338 (Pubitemid 44391875)
286. Snyder, A.W., D.J. Mitchell, L. Poladian, D.R. Rowland, and Y. Chen, 1991, " Physics of nonlinear fiber couplers, " J. Opt. Soc. Am. B 8, 2102. JOBPDE 0740-3224 10.1364/JOSAB.8.002102
287. Soljacic, M., and J.D. Joannopoulos, 2004, " Enhancement of nonlinear effects using photonic crystals, " Nature Mater. 3, 211. NMAACR 1476-1122 10.1038/nmat1097
288. Strecker, K.E., G.B. Partridge, A.G. Truscott, and R.G. Hulet, 2002, " Formation and propagation of matter-wave soliton trains, " Nature (London) NATUAS 0028-0836 417, 150. 10.1038/nature747 (Pubitemid 34506790)
289. Strecker, K.E., G.B. Partridge, A.G. Truscott, and R.G. Hulet, 2003, " Bright matter wave solitons in Bose-Einstein condensates, " New J. Phys. 5, 73. NJOPFM 1367-2630 10.1088/1367-2630/5/1/373
290. Sukhorukov, A.A., and Y.S. Kivshar, 2001, " Nonlinear localized waves in a periodic medium, " Phys. Rev. Lett. 87, 083901. PRLTAO 0031-9007 10.1103/PhysRevLett.87.083901
291. Sukhorukov, A.A., and Y.S. Kivshar, 2002 a, " Spatial optical solitons in nonlinear photonic crystals, " Phys. Rev. E PLEEE8 1063-651X 65, 036609. 10.1103/PhysRevE.65.036609 (Pubitemid 40629650)
292. Sukhorukov, A.A., and Y.S. Kivshar, 2002 b, " Nonlinear guided waves and spatial solitons in a periodic layered medium, " J. Opt. Soc. Am. B 19, 772. JOBPDE 0740-3224
293. Sukhorukov, A.A., Y.S. Kivshar, and O. Bang, 1999, " Two-color nonlinear localized photonic modes, " Phys. Rev. E PLEEE8 1063-651X 60, R41. 10.1103/PhysRevE.60.R41
294. Sukhorukov, A.A., Y.S. Kivshar, O. Bang, and C.M. Soukoulis, 2000, " Parametric localized modes in quadratic nonlinear photonic structures, " Phys. Rev. E PLEEE8 1063-651X 63, 016615. 10.1103/PhysRevE.63.016615
295. Sun, Z.-Y., Y.-T. Gao, X. Yu, and Y. Liu, 2011, " Amplification of nonautonomous solitons in the Bose-Einstein condensates and nonlinear optics, " Europhys. Lett. EULEEJ 0295-5075 93, 40004. 10.1209/0295-5075/93/40004
296. Suntsov, S., K.G. Makris, D.N. Christodoulides, G.I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, 2006, " Observation of discrete surface solitons, " Phys. Rev. Lett. 96, 063901. PRLTAO 0031-9007 10.1103/PhysRevLett.96.063901 (Pubitemid 43271064)
297. Susanto, H., P.G. Kevrekidis, R. Carretero-González, B.A. Malomed, and D.J. Frantzeskakis, 2007, " Mobility of discrete solitons in quadratically nonlinear media, " Phys. Rev. Lett. 99, 214103. PRLTAO 0031-9007 10.1103/PhysRevLett.99.214103 (Pubitemid 350159230)
298. Szameit, A., D. Blömer, J. Burghoff, T. Schreiber, T. Pertsch, S. Nolte, and A. Tünnermann, 2005, " Discrete nonlinear localization in femtosecond laser written waveguides in fused silica, " Opt. Express 13, 10552. OPEXFF 1094-4087 10.1364/OPEX.13.010552 (Pubitemid 41832641)
299. Szameit, A., J. Burghoff, T. Pertsch, S. Nolte, A. Tünnermann, and F. Lederer, 2006, " Two-dimensional soliton in cubic fs laser written waveguide arrays in fused silica, " Opt. Express 14, 6055. OPEXFF 1094-4087 10.1364/OE.14.006055
300. Szameit, A., I.L. Garanovich, M. Heinrich, A.A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and Y.S. Kivshar, 2009 a, " Polychromatic dynamic localization in curved photonic lattices, " Nature Phys. 5, 271. NPAHAX 1745-2473 10.1038/nphys1221
301. Szameit, A., Y.V. Kartashov, F. Dreisow, M. Heinrich, T. Pertsch, S. Nolte, A. Tünnermann, V.A. Vysloukh, F. Lederer, and L. Torner, 2009 b, " Inhibition of light tunneling in waveguide arrays, " Phys. Rev. Lett. 102, 153901. PRLTAO 0031-9007 10.1103/PhysRevLett.102.153901
302. Szameit, A., Y.V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and L. Torner, 2007, " Observation of surface solitons in asymmetric waveguide arrays, " Phys. Rev. Lett. 98, 173903. PRLTAO 0031-9007 10.1103/PhysRevLett.98.173903 (Pubitemid 46676944)
303. Tang, X.Y., Y. Gao, and P.K. Shukla, 2010, " Vector solitons of a one-dimensional spatially inhomogeneous coupled nonlinear Schrödinger equation with a double well potential, " Eur. Phys. J. D EPJDF6 1434-6060 61, 677. 10.1140/epjd/e2010-09660-y
304. Tang, X.-Y., and P.K. Shukla, 2007, " Solution of the one-dimensional spatially inhomogeneous cubic-quintic nonlinear Schrödinger equation with an external potential, " Phys. Rev. A 76, 013612. PLRAAN 1050-2947 10.1103/PhysRevA.76.013612 (Pubitemid 47117026)
305. Theis, M., G. Thalhammer, K. Winkler, M. Hellwig, G. Ruff, R. Grimm, and J.H. Denschlag, 2004, " Tuning the scattering length with an optically induced Feshbach resonance, " Phys. Rev. Lett. 93, 123001. PRLTAO 0031-9007 10.1103/PhysRevLett.93.123001
306. Theocharis, G., P. Schmelcher, P.G. Kevrekidis, and D.J. Frantzeskakis, 2005, " Matter-wave solitons of collisionally inhomogeneous condensates, " Phys. Rev. A 72, 033614. PLRAAN 1050-2947 10.1103/PhysRevA.72.033614 (Pubitemid 41782083)
307. Theocharis, G., P. Schmelcher, P.G. Kevrekidis, and D.J. Frantzeskakis, 2006, " Dynamical trapping and transmission of matter-wave solitons in a collisionally inhomogeneous environment, " Phys. Rev. A 74, 053614. PLRAAN 1050-2947 10.1103/PhysRevA.74.053614 (Pubitemid 44749243)
308. Tian, Q., L. Wu, J.-F. Zhang, B.A. Malomed, D. Mihalache, and W.M. Liu, 2011, " Exact solitons and their stability control in the nonlinear Schrödinger equation with spatiotemporally modulated nonlinearity, " 2011, Phys. Rev. E PLEEE8 1539-3755 83, 016602. 10.1103/PhysRevE.83.016602
309. Torner, L., S. Carrasco, J.P. Torres, L.-C. Crasovan, and D. Mihalache, 2001, " Tandem light bullets, " Opt. Commun. 199, 277. OPCOB8 0030-4018 10.1016/S0030-4018(01)01573-5 (Pubitemid 33039473)
310. Torner, L., and Y.V. Kartashov, 2009, " Light bullets in optical tandems, " Opt. Lett. 34, 1129. OPLEDP 0146-9592 10.1364/OL.34.001129
311. Torruellas, W.E., Z. Wang, D.J. Hagan, E.W. VanStryland, G.I. Stegeman, L. Torner, and C.R. Menyuk, 1995, " Observation of two-dimensional spatial solitary waves in a quadratic medium, " Phys. Rev. Lett. 74, 5036. PRLTAO 0031-9007 10.1103/PhysRevLett.74.5036
312. Towers, I., and B.A. Malomed, 2002, " Stable (2 + 1) -dimensional solitons in a layered medium with sign-alternating Kerr nonlinearity, " J. Opt. Soc. Am. B JOBPDE 0740-3224 19, 537 10.1364/JOSAB.19.000537.
313. Tsang, C.H., B.A. Malomed, and K.W. Chow, 2011, " Exact solutions for periodic and solitary matter waves in nonlinear lattices, " Discrete Contin. Dyn. Syst. Ser. S 1937-1179 4, 1299 10.3934/dcdss.2011.4.1299.
314. Tsang, C.H., B.A. Malomed, C.-K. Lam, and K.W. Chow, 2010, " Solitons pinned to hot spots, " Eur. Phys. J. D EPJDF6 1434-6060 59, 81. 10.1140/epjd/e2010-00073-0
315. Vakhitov, M., and A. Kolokolov, 1973, " Stationary solutions of the wave equation in a medium with nonlinearity saturation, " Radiophys. Quantum Electron. RPQEAC 0033-8443 16, 783. 10.1007/BF01031343
316. Vinetskii, V.O., and N.V. Kukhtarev, 1974, " Theory of conductivity induced by recording of holographic lattices in nonmetallic crystals, " Fiz. Tverd. Tela (Kharkov) FZTTAA 0015-3249 16, 3714
317. [Vinetskii, V.O. N.V. Kukhtarev Sov. Phys. Solid State 16, 2414 (1975)]. SPSSA7 0038-5654
318. Wang, C., P.G. Kevrekidis, N. Whitaker, D.J. Frantzeskakis, S. Middelkamp, and P. Schmelcher, 2009, " Collisionally inhomogeneous Bose-Einstein condensates in double-well potentials, " Physica D (Amsterdam) 238, 1362. PDNPDT 0167-2789 10.1016/j.physd.2008.11.003
319. Wang, C., P.G. Kevrekidis, N. Whitaker and B.A. Malomed, 2008, " Two-component nonlinear Schrödinger models with a double-well potential, " Physica D (Amsterdam) 237, 2922. PDNPDT 0167-2789 10.1016/j.physd.2008. 04.023
320. Wang, C., G. Theocharis, P.G. Kevrekidis, N. Whitaker, K.J.H. Law, D.J. Frantzeskakis, and B.A. Malomed, 2009, " Two-dimensional paradigm for symmetry breaking: The nonlinear Schroedinger equation with a four-well potential, " Phys. Rev. E PLEEE8 1539-3755 80, 046611. 10.1103/PhysRevE.80. 046611
321. Wang, D.S., X.H. Hu, J. Hu, and W.M. Liu, 2010, " Quantized quasi-two-dimensional Bose-Einstein condensates with spatially modulated nonlinearity, " Phys. Rev. A 81, 025604. PLRAAN 1050-2947 10.1103/PhysRevA.81.025604
322. Wang, J., J. Yang, T.J. Alexander, and Y.S. Kivshar, 2009, " Truncated-Bloch wave solitons in optical lattices, " Phys. Rev. A 79, 043610. PLRAAN 1050-2947 10.1103/PhysRevA.79.043610
323. Wang, X., A. Bezryadina, Z. Chen, K.G. Makris, D.N. Christodoulides, and G.I. Stegeman, 2007, " Observation of two-dimensional surface solitons, " Phys. Rev. Lett. 98, 123903. PRLTAO 0031-9007 10.1103/PhysRevLett.98. 123903 (Pubitemid 46474057)
324. Wang, X., Z. Chen, J. Wang, and J. Yang, 2007, " Observation of in-band lattice solitons, " Phys. Rev. Lett. 99, 243901. PRLTAO 0031-9007 10.1103/PhysRevLett.99.243901 (Pubitemid 350276608)
325. Wu, B., and Q. Niu, 2001, " Landau and dynamical instabilities of the superflow of Bose-Einstein condensates in optical lattices, " Phys. Rev. A PLRAAN 1050-2947 64, 061603. 10.1103/PhysRevA.64.061603
326. Wu, L., Lu Li, J.-F. Zhang, D. Mihalache, B.A. Malomed, and W.M. Liu, 2010, " Exact solutions of the Gross-Pitaevskii equation for stable vortex modes in two-dimensional Bose-Einstein condensates, " Phys. Rev. A 81, 061805(R). PLRAAN 1050-2947 10.1103/PhysRevA.81.061805
327. Xie, P., Z.Q. Zhang, and X. Zhang, 2003, " Gap solitons and soliton trains in finite-sized two-dimensional periodic and quasi-periodic photonic crystals, " Phys. Rev. E PLEEE8 1063-651X 67, 026607. 10.1103/PhysRevE.67. 026607
328. Yablonovitch, E., 1987, " Inhibited spontaneous emission in solid-state physics and electronics, " Phys. Rev. Lett. 58, 2059. PRLTAO 0031-9007 10.1103/PhysRevLett.58.2059
329. Yablonovitch, E., 1994, " Photonic crystals, " J. Mod. Opt. JMOPEW 0950-0340 41, 173. 10.1080/09500349414550261
330. Yablonovitch, E., 2001, " Photonic crystals: Semiconductors of light, " Sci. Am. 285, 46. SCAMAC 0036-8733 10.1038/scientificamerican1201- 46
331. Yablonovitch, E., T.J. Gmitter, and K.M. Leung, 1991, " Photonic-band structure-the face-centered-cubic case employing nonspherical atoms, " Phys. Rev. Lett. 67, 2295. PRLTAO 0031-9007 10.1103/PhysRevLett. 67.2295
332. Yan, Z., 2010, " Nonautonomous rogons in the inhomogeneous nonlinear Schrödinger equation with variable coefficients, " Phys. Lett. A 374, 672. PYLAAG 0375-9601 10.1016/j.physleta.2009.11.030
333. Yan, Z., and V.V. Konotop, 2009, " Exact solutions to three-dimensional generalized nonlinear Schrödinger equations with varying potential and nonlinearities, " Phys. Rev. E PLEEE8 1539-3755 80, 036607. 10.1103/PhysRevE.80.036607
334. Yanay, H., L. Khaykovich, and B.A. Malomed, 2009, " Stabilization and destabilization of second-order solitons against perturbations in the nonlinear Schrödinger equation, " Chaos 19, 033145. CHAOEH 1054-1500 10.1063/1.3238246
335. Yang, J., and Z.H. Musslimani, 2003, " Fundamental and vortex solitons in a two-dimensional optical lattice, " Opt. Lett. 28, 2094. OPLEDP 0146-9592 10.1364/OL.28.002094
336. Ye, F., Y.V. Kartashov, B. Hu, and L. Torner, 2009, " Light bullets in Bessel optical lattices with spatially modulated nonlinearity, " Opt. Express 17, 11328. OPEXFF 1094-4087 10.1364/OE.17.011328
337. Ye, F., Y.V. Kartashov, and L. Torner, 2006, " Asymmetric matter-wave solitons at nonlinear interfaces, " Phys. Rev. A 74, 063616. PLRAAN 1050-2947 10.1103/PhysRevA.74.063616 (Pubitemid 44927216)
338. Ye, F., D. Mihalache, B. Hu, and N.-C. Panoiu, 2010, " Subwavelength plasmonic lattice solitons in arrays of metallic nanowires, " Phys. Rev. Lett. 104, 106802. PRLTAO 0031-9007 10.1103/PhysRevLett.104.106802
339. Zabusky, N., and M. Kruskal, 1965, " Interaction of solitons in a collisionless plasma and the recurrence of initial states, " Phys. Rev. Lett. 15, 240. PRLTAO 0031-9007 10.1103/PhysRevLett.15.240
340. Zafrany, A., B.A. Malomed, and I.M. Merhasin, 2005, " Solitons in a linearly coupled system with separated dispersion and nonlinearity, " Chaos 15, 037108. CHAOEH 1054-1500 10.1063/1.1894705 (Pubitemid 43127592)
341. Zezyulin, D.A., G.L. Alfimov, V.V. Konotop, and V.M. Perez-Garcia, 2007, " Control of nonlinear modes by scattering-length management in Bose-Einstein condensates, " Phys. Rev. A 76, 013621. PLRAAN 1050-2947 10.1103/PhysRevA.76.013621 (Pubitemid 47120828)
342. Zhang, J.-F., Y.-S. Li, J. Meng, L. Wu, and B.A. Malomed, 2010, " Matter-wave solitons and finite-amplitude Bloch waves in optical lattices with a spatially modulated nonlinearity, " Phys. Rev. A PLRAAN 1050-2947 82, 033614. 10.1103/PhysRevA.82.033614
343. Zhou, J., C. Xue, Y. Qi, and S. Lou, 2008, " Soliton control in optical lattices with periodic modulation of nonlinearity coefficient, " Phys. Lett. A 372, 4395. PYLAAG 0375-9601 10.1016/j.physleta.2008.04.003