Dark solitons in dynamical lattices with the cubic-quintic nonlinearity

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

Volumn 76, Issue 4, 2007, Pages

  Maluckov, Aleksandra ^a   Hadčievski, Ljupčo ^b   Malomed, Boris A ^c  

^a UNIVERSITY OF NI   (Serbia)

^b UNIVERSITY OF BELGRADE   (Serbia)

^c TEL AVIV UNIVERSITY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; EIGENVALUES AND EIGENFUNCTIONS; MATHEMATICAL MODELS; OPTICAL WAVEGUIDES; PERTURBATION TECHNIQUES; WAVE EQUATIONS;

CUBIC-QUINTIC NONLINEARITY; DARK SOLITONS; DYNAMICAL LATTICES; STATIC SOLITONS;

SOLITONS;

EID: 35248826538     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.76.046605     Document Type: Article

References (65)

1. P. G. Kevrekidis, K. Ø. Rasmussen, and A. R. Bishop, Int. J. Mod. Phys. B IJPBEV 0217-9792 10.1142/S0217979201007105 15, 2833 (2001).
2. Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, San Diego, 2003).
3. D. N. Christodoulides and R. I. Joseph, Opt. Lett. OPLEDP 0146-9592 13, 794 (1988).
4. H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.81.3383 81, 3383 (1998).
5. D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature (London) NATUAS 0028-0836 10.1038/nature01936 424, 817 (2003).
6. J. W. Fleischer, G. Bartal, O. Cohen, T. Schwartz, O. Manela, B. Freedman, M. Segev, H. Buljan, and N. K. Efremidis, Opt. Express OPEXFF 1094-4087 10.1364/OPEX.13.001780 13, 1780 (2005).
7. M. J. Ablowitz, Z. H. Musslimani, and G. Biondini, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.65.026602 65, 026602 (2002).
8. I. E. Papacharalampous, P. G. Kevrekidis, B. A. Malomed, and D. J. Frantzeskakis, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.68.046604 68, 046604 (2003).
9. J. Meier, G. I. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.093903 93, 093903 (2004);
10. J. Meier, Opt. Express OPEXFF 1094-4087 10.1364/OPEX.13.001797 13, 1797 (2005);
11. Y. Linzon, Y. Sivan, B. Malomed, M. Zaezjev, R. Morandotti, and S. Bar-Ad, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.193901 97, 193901 (2006).
12. D. Cheskis, S. Bar-Ad, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, and D. Ross, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.223901 91, 223901 (2003).
13. A. Trombettoni and A. Smerzi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.2353 86, 2353 (2001);
14. G. L. Alfimov, P. G. Kevrekidis, V. V. Konotop, and M. Salerno, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.66.046608 66, 046608 (2002);
15. R. Carretero-González and K. Promislow, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.66.033610 66, 033610 (2002).
16. F. S. Cataliotti, S. Burger, C. Fort, P. Maddaloni, F. Minardi, A. Trombettoni, A. Smerzi, and M. Inguscio, Science SCIEAS 0036-8075 10.1126/science.1062612 293, 843 (2001);
17. M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, Nature (London) NATUAS 0028-0836 10.1038/415039a 415, 39 (2002).
18. M. A. Porter, R. Carretero-González, P. G. Kevrekidis, and B. A. Malomed, Chaos CHAOEH 1054-1500 10.1063/1.1858114 15, 015115 (2005).
19. S. Aubry, Physica D PDNPDT 0167-2789 10.1016/S0167-2789(96)00261-8 103D, 201 (1997);
20. R. S. MacKay and S. Aubry, Nonlinearity NONLE5 0951-7715 10.1088/0951-7715/7/6/006 7, 1623 (1994);
21. S. Flach and C. R. Willis, Phys. Rep. PRPLCM 0370-1573 10.1016/S0370-1573(97)00068-9 295, 181 (1998);
22. G. P. Tsironis, Chaos CHAOEH 1054-1500 10.1063/1.1557234 13, 657 (2003);
23. D. K. Campbell, S. Flach, and Y. S. Kivshar, Phys. Today PHTOAD 0031-9228 57 (1), 43 (2004).
24. M. Stepić, D. Kip, L. Hadčievski, and A. Maluckov, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.69.066618 69, 066618 (2004);
25. L. Hadčievski, A. Maluckov, M. Stepić, and D. Kip, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.033901 93, 033901 (2004).
26. A. Khare, K. Ø. Rasmussen, M. R. Samuelsen, and A. Saxena, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/38/4/002 38, 807 (2005).
27. V. O. Vinetskii and N. V. Kukhtarev, Fiz. Tverd. Tela (Leningrad) FTVTAC 0367-3294 16, 3714 (1974)
28. V. O. Vinetskii and N. V. Kukhtarev, [Sov. Phys. Solid State SPSSA7 0038-5654 16, 2414 (1975)].
29. F. Chen, M. Stepić, C. E. Ruter, D. Runde, D. Kip, V. Shandarov, O. Manela, and M. Segev, Opt. Express OPEXFF 1094-4087 10.1364/OPEX.13.004314 13, 4314 (2005).
30. J. Dorignac, J. C. Eilbeck, M. Salerno, and A. C. Scott, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.025504 93, 025504 (2004).
31. M. Johansson and Yu. S. Kivshar, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.82.85 82, 85 (1999);
32. R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.3296 86, 3296 (2001);
33. D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.093904 92, 093904 (2004);
34. B. Sanchez-Rey and M. Johansson, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.71.036627 71, 036627 (2005);
35. H. Susanto and M. Johansson, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.72.016605 72, 016605 (2005).
36. E. Smirnov, C. E. Ruter, M. Stepic, D. Kip, and V. Shandarov, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.74.065601 74, 065601 (R) (2006).
37. E. P. Fitrakis, P. G. Kevrekidis, H. Susanto, and D. J. Frantzeskakis, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.75.066608 75, 066608 (2007).
38. L. Hadzievski, A. Maluckov, and M. Stepic, Opt. Express OPEXFF 1094-4087 10.1364/OE.15.005687 15, 5687 (2007).
39. F. Smektala, C. Quemard, V. Couderc, and A. Barthélémy, J. Non-Cryst. Solids JNCSBJ 0022-3093 10.1016/S0022-3093(00)00215-5 274, 232 (2000);
40. G. Boudebs, S. Cherukulappurath, H. Leblond, J. Troles, F. Smektala, and F. Sanchez, Opt. Commun. OPCOB8 0030-4018 10.1016/S0030-4018(03)01341-5 219, 427 (2003);
41. C. Zhan, D. Zhang, D. Zhu, D. Wang, Y. Li, D. Li, Z. Lu, L. Zhao, and Y. Nie, J. Opt. Soc. Am. B JOBPDE 0740-3224 10.1364/JOSAA.19.000369 19, 369 (2002).
42. I. M. Merhasin, B. V. Gisin, R. Driben, and B. A. Malomed, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.71.016613 71, 016613 (2005);
43. J. Wang, F. Ye, L. Dong, T. Cai, and Y.-P. Li, Phys. Lett. A PYLAAG 0375-9601 10.1016/j.physleta.2005.03.024 339, 74 (2005).
44. R. Carretero-González, J. D. Talley, C. Chong, and B. A. Malomed, Physica D PDNPDT 0167-2789 10.1016/j.physd.2006.01.022 216, 77 (2006).
45. D. Mihalache, D. Mazilu, F. Lederer, L.-C. Crasovan, Y. V. Kartashov, L. Torner, and B. A. Malomed, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.74. 066614 74, 066614 (2006).
46. B. A. Malomed and M. I. Weinstein, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(96)00516-6 220, 91 (1996).
47. Kh. I. Pushkarov and D. I. Pushkarov, and I. V. Tomov, Opt. Quantum Electron. OQELDI 0306-8919 10.1007/BF00620372 11, 471 (1979);
48. Kh. I. Pushkarov and D. I. Pushkarov, Rep. Math. Phys. RMHPBE 0034-4877 10.1016/0034-4877(80)90074-9 17, 37 (1980);
49. S. Cowan, R. H. Enns, S. S. Rangnekar, and S. S. Sanghera, Can. J. Phys. CJPHAD 0008-4204 64, 311 (1986);
50. J. Herrmann, Opt. Commun. OPCOB8 0030-4018 10.1016/0030-4018(92)90006-D 87, 161 (1992).
51. Yu. S. Kivshar and B. Luther-Davies, Phys. Rep. PRPLCM 0370-1573 10.1016/S0370-1573(97)00073-2 298, 81 (1998).
52. I. V. Barashenkov and V. G. Makhankov, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(88)91042-0 128, 52 (1988);
53. I. V. Barashenkov, A. D. Gocheva, V. G. Makhankov, and I. V. Puzynin, Physica D PDNPDT 0167-2789 10.1016/0167-2789(89)90237-6 34, 240 (1988).
54. D. E. Pelinovsky, Y. S. Kivshar, and V. V. Afanasjev, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.54.2015 54, 2015 (1996);
55. S. Tanev and D. I. Pushkarov, Opt. Commun. OPCOB8 0030-4018 10.1016/S0030-4018(97)00230-7 141, 322 (1997);
56. H. W. Schürmann and V. S. Serov, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.62.2821 62, 2821 (2000);
57. D. J. Frantzeskakis, P. G. Kevrekidis, and N. P. Proukakis, Phys. Lett. A PYLAAG 0375-9601 10.1016/j.physleta.2006.11.074 364, 129 (2007).
58. I. V. Barashenkov, T. L. Boyadjiev, I. V. Puzynin, and T. Zhanlav, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(89)90658-0 135, 125 (1989);
59. I. V. Barashenkov, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett. 77.1193 77, 1193 (1996).
60. S. González-Pérez-Sandi, J. Fujioka, and B. A. Malomed, Physica D PDNPDT 0167-2789 10.1016/j.physd.2004.06.009 197, 86 (2004).
61. K. Maruno, A. Ankiewicz, and N. Akhmediev, Phys. Lett. A PYLAAG 0375-9601 10.1016/j.physleta.2005.08.028 347, 231 (2005);
62. C. Q. Dai and J. F. Zhang, Opt. Commun. OPCOB8 0030-4018 10.1016/j.optcom.2006.01.033 263, 309 (2006).
63. Y. S. Kivshar and M. Peyrard, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.46.3198 46, 3198 (1992).
64. S. Aubry, Physica D PDNPDT 0167-2789 10.1016/0167-2789(94)90190-2 71, 196 (1994).
65. T. R. O. Melvin, A. R. Champneys, P. G. Kevrekidis, and J. Cuevas, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.124101 97, 124101 (2006).