Discrete solitons and vortices on anisotropic lattices

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 72, Issue 4, 2005, Pages

  Kevrekidis, P G ^a   Frantzeskakis, D J ^b   Carretero Gonzalez R ^c   Malomed, B A ^d   Bishop, A R ^e  

^a UNIVERSITY OF MASSACHUSETTS   (United States)

^b UNIVERSITY OF ATHENS   (Greece)

^c SAN DIEGO STATE UNIVERSITY   (United States)

^d TEL AVIV UNIVERSITY   (Israel)

^e LOS ALAMOS NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DISCRETE SOLITONS; LYAPUNOV-SCHMIDT THEORY; NONLINEAR LATTICES; VORTEX SOLITONS;

ANISOTROPY; APPROXIMATION THEORY; MATHEMATICAL MODELS; NUMERICAL METHODS; VARIATIONAL TECHNIQUES; VORTEX FLOW;

SOLITONS;

EID: 28944451932     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.72.046613     Document Type: Article

References (60)

1. S. Aubry, Physica D PDNPDT 0167-2789 10.1016/S0167-2789(96)00261-8 103, 201 (1997);
2. S. Flach and C. R. Willis, Phys. Rep. PRPLCM 0370-1573 10.1016/S0370-1573(97)00068-9 295, 181 (1998);
3. D. Hennig and G. Tsironis, Phys. Rep. PRPLCM 0370-1573 10.1016/S0370-1573(98)00025-8 307, 333 (1999);
4. P. G. Kevrekidis, K. Ø. Rasmussen, and A. R. Bishop, Int. J. Mod. Phys. B IJPBEV 0217-9792 10.1142/S0217979201007105 15, 2833 (2001).
5. D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature (London) NATUAS 0028-0836 10.1038/nature01936 424, 817 (2003);
6. Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, San Diego, CA, 2003).
7. P. G. Kevrekidis and D. J. Frantzeskakis, Mod. Phys. Lett. B MPLBET 0217-9849 10.1142/S0217984904006809 18, 173 (2004);
8. V. V. Konotop and V. A. Brazhnyi, Mod. Phys. Lett. B MPLBET 0217-9849 10.1142/S0217984904007190 18, 627 (2004);
9. P. G. Kevrekidis, R. Carretero-González, D. J. Frantzeskakis, and I. G. Kevrekidis, Mod. Phys. Lett. B MPLBET 0217-9849 18, 1481 (2004).
10. M. Sato and A. J. Sievers, Nature (London) NATUAS 0028-0836 10.1038/nature03038 432, 486 (2004);
11. M. Sato, B. E. Hubbard, A. J. Sievers, B. Ilic, and H. G. Craighead, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2003-10224-x 66, 318 (2004);
12. M. Sato, B. E. Hubbard, A. J. Sievers, B. Ilic, D. A. Czaplewski, and H. G. Craighead, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.044102 90, 044102 (2003).
13. M. Peyrard, Nonlinearity NONLE5 0951-7715 10.1088/0951-7715/17/2/R01 17, R1 (2004).
14. N. Voglis, Mon. Not. R. Astron. Soc. MNRAA4 0035-8711 10.1046/j.1365-8711.2003.06848.x 344, 575 (2003).
15. N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.66.046602 66, 046602 (2002);
16. A. A. Sukhorukov, Yu. S. Kivshar, H. S. Eisenberg, and Y. Silberberg, IEEE J. Quantum Electron. IEJQA7 0018-9197 10.1109/JQE.2002.806184 39, 31 (2003).
17. B. A. Malomed and P. G. Kevrekidis, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.64.026601 64, 026601 (2001).
18. B. B. Baizakov, B. A. Malomed, and M. Salerno, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2003-00579-4 63, 642 (2003).
19. J. Yang and Z. Musslimani, Opt. Lett. OPLEDP 0146-9592 23, 2094 (2003);
20. P. G. Kevrekidis, B. A. Malomed, Z. Chen, and D. J. Frantzeskakis, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.70.056612 70, 056612 (2004).
21. J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90. 023902 90, 023902 (2003);
22. H. Martin, E. D. Eugenieva, Z. G. Chen, and D. N. Christodoulides, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.123902 92, 123902 (2004);
23. J. K. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, Opt. Lett. OPLEDP 0146-9592 10.1364/OL.29.001662 29, 1662 (2004);
24. Z. G. Chen, H. Martin, E. D. Eugenieva, J. J. Xu, and A. Bezryadina, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.143902 92, 143902 (2004)
25. Z. G. Chen, A. Bezryadina, I. Makasyuk and J. K. Yang, Opt. Lett. OPLEDP 0146-9592 10.1364/OL.29.001656 29, 1656 (2004);
26. J. Yang, I. Makasyuk I, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. G. Chen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.113902 94, 113902 (2005).
27. D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Yu. S. Kivshar, H. Martin, I. Makasyuk, and Z. G. Chen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.123903 92, 123903 (2004);
28. J. W. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D. N. Christodoulides, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.123904 92, 123904 (2004).
29. S. Burger, K. Bongs, S. Dettmer, W. Ertmer, K. Sengstock, A. Sanpera, G. V. Shlyapnikov, and M. Lewenstein, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.83.5198 83, 5198 (1999);
30. J. Denschlag, J. E. Simsarian, D. L. Feder, C. W. Clark, L. A. Collins, J. Cubizolles, L. Deng, E. W. Hagley, K. Helmerson, W. P. Reinhardt, S. L. Rolston, B. I. Schneider, and W. D. Phillips, Science SCIEAS 0036-8075 10.1126/science.287.5450.97 287, 97 (2000);
31. B. P. Anderson, P. C. Haljan, C. A. Regal, D. L. Feder, L. A. Collins, C. W. Clark, and E. A. Cornell, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.2926 86, 2926 (2001).
32. K. E. Strecker, G. B. Partridge, A. G. Truscott, and R. G. Hulet, Nature (London) NATUAS 0028-0836 10.1038/nature747 417, 150 (2002);
33. L. Khaykovich, F. Schreck, G. Ferrari, T. Bourdel, J. Cubizolles, L. D. Carr, Y. Castin, and C. Salomon, Science SCIEAS 0036-8075 10.1126/science.1071021 296, 1290 (2002).
34. B. Eiermann, Th. Anker, M. Albiez, M. Taglieber, P. Treutlein, K.-P. Marzlin, and M. K. Oberthaler, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.230401 92, 230401 (2004).
35. B. B. Baizakov, B. A. Malomed, and M. Salerno, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2003-00579-4 63, 642 (2003);
36. B. B. Baizakov, B. A. Malomed, and M. Salerno, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.70.053613 70, 053613 (2004).
37. See, e.g., M. Greiner, I. Bloch, O. Mandel, T. W. Hansch, and T. Esslinger, Appl. Phys. B: Lasers Opt. APBOEM 0946-2171 10.1007/s003400100744 73, 769 (2001);
38. M. Greiner, I. Bloch, O. Mandel, T. W. Hansch, and T. Esslinger, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.4447 87, 160405 (2001).
39. R. S. MacKay and S. Aubry, Nonlinearity NONLE5 0951-7715 10.1088/0951-7715/7/6/006 7, 1623 (1994).
40. M. G. Vakhitov and A. A. Kolokolov, Izv. Vuz. Radiofiz. 16, 1020 (1973)
41. M. G. Vakhitov and A. A. Kolokolov, [Sov. J. Radiophys. Quantum Electr. 16, 783 (1973)];
42. L. Bergé, Phys. Rep. PRPLCM 0370-1573 303, 260 (1998).
43. B. B. Baizakov, B. A. Malomed, and M. Salerno, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2003-00579-4 63, 642 (2003);
44. B. B. Baizakov, B. A. Malomed, and M. Salerno, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.70.053613 70, 053613 (2004).
45. B. B. Baizakov, M. Salerno, and B. A. Malomed, in Nonlinear Waves: Classical and Quantum Aspects, edited by, F. Kh. Abdullaev, and, V. V. Konotop, (Kluwer Academic Publishers, Dordrecht, 2004), p. 61;
46. also available at http://rsphy2.anu.edu.au/~asd124/-Baizakov_2004_61_NonlinearWaves.pdf.
47. B. A. Malomed and M. I. Weinstein, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(96)00516-6 220, 91 (1996).
48. M. I. Weinstein, Nonlinearity NONLE5 0951-7715 10.1088/0951-7715/12/3/ 314 12, 673 (1999).
49. S. Flach, K. Kladko, and R. S. MacKay, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.78.1207 78, 1207 (1997);
50. P. G. Kevrekidis, K. Ø. Rasmussen, and A. R. Bishop, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.61.2006 61, 2006 (2000);
51. P. G. Kevrekidis, K. Ø. Rasmussen, and A. R. Bishop, Math. Comput. Simul. MCSIDR 0378-4754 10.1016/S0378-4754(00)00298-6 55, 449 (2001).
52. J.-C. van der Meer, Nonlinearity NONLE5 0951-7715 10.1088/0951-7715/3/4/005 3, 1041 (1990).
53. S. Darmanyan, A. Kobyakov, and F. Lederer, JETP JTPHES 1063-7761 10.1134/1.558526 86, 682 (1998);
54. P. G. Kevrekidis, A. R. Bishop, and K. Ø. Rasmussen, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.63.036603 63, 036603 (2001).
55. D. E. Pelinovsky, P. G. Kevrekidis, and D. J. Frantzeskakis, e-print nlin.PS/0411016;
56. Physica D PDNPDT 0167-2789 (to be published).
57. M. Golubitsky and D. G. Schaeffer, Singularities and Groups in Bifurcation Theory (Springer-Verlag, New York, 1985), Vol. 1.
58. T. Pertsch, U. Peschel, F. Lederer, J. Burghoff, M. Will, S. Nolte, and A. Tunnermann, Opt. Lett. OPLEDP 0146-9592 10.1364/OL.29.000468 29, 468 (2004).
59. P. G. Kevrekidis, B. A. Malomed, D. J. Frantzeskakis, and R. Carretero-González, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.080403 93, 080403 (2004);
60. R. Carretero-González, P. G. Kevrekidis, B. A. Malomed, and D. J. Frantzeskakis, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.203901 94, 203901 (2005).