Pattern formation by kicked solitons in the two-dimensional Ginzburg-Landau medium with a transverse grating

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

Volumn 87, Issue 1, 2013, Pages

  Besse, Valentin ^a   Leblond, Hervé ^a   Mihalache, Dumitru ^a,b,c   Malomed, Boris A ^d  

^a UNIVERSITÉ D'ANGERS   (France)

^b HORIA HULUBEI NATIONAL INSTITUTE OF PHYSICS AND NUCLEAR ENGINEERING   (Romania)

^c ACADEMY OF ROMANIAN SCIENTISTS   (Romania)

^d TEL AVIV UNIVERSITY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

ANALYTICAL APPROXIMATION; COMPLEX GINZBURG-LANDAU EQUATION; DEPINNING; DIFFERENT SIZES; DISSIPATIVE SOLITONS; ELASTIC AND INELASTIC COLLISIONS; FREELY MOVING; GINZBURG-LANDAU; INDUCED MOBILITY; PATTERN FORMATION; PERIODIC POTENTIALS; SYSTEMATIC SIMULATION;

NONLINEAR EQUATIONS; TWO DIMENSIONAL;

SOLITONS;

ARTICLE; COMPUTER SIMULATION; LASER; METHODOLOGY; RADIATION SCATTERING; REFRACTOMETRY; THEORETICAL MODEL;

COMPUTER SIMULATION; LASERS; MODELS, THEORETICAL; REFRACTOMETRY; SCATTERING, RADIATION;

EID: 84873032315     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.87.012916     Document Type: Article

References (83)

1. N. N. Rosanov, Vario Spatial Hysteresis and Optical Patterns (Springer, Berlin, 2002).
2. S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger, Nature (London) NATUAS 0028-0836 10.1038/nature01049 419, 699 (2002); (Pubitemid 35177950)
3. Z. Bakonyi, D. Michaelis, U. Peschel, G. Onishchukov, and F. Lederer, J. Opt. Soc. Am. B JOBPDE 0740-3224 10.1364/JOSAB.19.000487 19, 487 (2002);
4. E. A. Ultanir, G. I. Stegeman, D. Michaelis, C. H. Lange, and F. Lederer, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.253903 90, 253903 (2003);
5. P. Mandel and M. Tlidi, J. Opt. B JOBOFD 1464-4266 10.1088/1464-4266/6/9/ R02 6, R60 (2004);
6. N. N. Rosanov, S. V. Fedorov, and A. N. Shatsev, Appl. Phys. B APBOEM 0946-2171 10.1007/s00340-005-1981-4 81, 937 (2005); (Pubitemid 41660655)
7. C. O. Weiss and Ye. Larionova, Rep. Prog. Phys. RPPHAG 0034-4885 10.1088/0034-4885/70/2/R03 70, 255 (2007);
8. N. Veretenov and M. Tlidi, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.80.023822 80, 023822 (2009);
9. P. Genevet, S. Barland, M. Giudici, and J. R. Tredicce, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.104.223902 104, 223902 (2010).
10. N. Lazarides and G. P. Tsironis, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.71.036614 71, 036614 (2005); (Pubitemid 40619885)
11. Y. M. Liu, G. Bartal, D. A. Genov, and X. Zhang, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.153901 99, 153901 (2007); (Pubitemid 47569117)
12. E. Feigenbaum and M. Orenstein, Opt. Lett. OPLEDP 0146-9592 10.1364/OL.32.000674 32, 674 (2007); (Pubitemid 46363472)
13. I. R. Gabitov, A. O. Korotkevich, A. I. Maimistov, and J. B. Mcmahon, Appl. Phys. A APAMFC 0947-8396 10.1007/s00339-007-4102-x 89, 277 (2007); (Pubitemid 47319461)
14. A. R. Davoyan, I. V. Shadrivov, and Y. S. Kivshar, Opt. Express OPEXFF 1094-4087 10.1364/OE.17.021732 17, 21732 (2009);
15. K. Y. Bliokh, Y. P. Bliokh, and A. Ferrando, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.79.041803 79, 041803 (2009);
16. E. V. Kazantseva and A. I. Maimistov, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.79.033812 79, 033812 (2009);
17. Y.-Y. Lin, R.-K. Lee, and Y. S. Kivshar, Opt. Lett. OPLEDP 0146-9592 10.1364/OL.34.002982 34, 2982 (2009);
18. A. Marini and D. V. Skryabin, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.81.033850 81, 033850 (2010);
19. A. Marini, D. V. Skryabin, and B. A. Malomed, Opt. Express OPEXFF 1094-4087 10.1364/OE.19.006616 19, 6616 (2011).
20. Dissipative Solitons, edited by N. Akhmediev and A. Ankiewicz, Lecture Notes in Physics, Vol. 661 (Springer, Berlin, 2005);
21. Dissipative Solitons: From Optics to Biology and Medicine, edited by N. Akhmediev and A. Ankiewicz, Lecture Notes in Physics, Vol. 751 (Springer, Berlin, 2008).
22. J. Anglin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.79.6 79, 6 (1997);
23. F. T. Arecchi, J. Bragard, and L. M. Castellano, Opt. Commun. OPCOB8 0030-4018 10.1016/S0030-4018(99)00670-7 179, 149 (2000);
24. J. Keeling and N. G. Berloff, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100.250401 100, 250401 (2008);
25. B. A. Malomed, O. Dzyapko, V. E. Demidov, and S. O. Demokritov, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.81.024418 81, 024418 (2010);
26. H. Deng, H. Haug, and Y. Yamamoto, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.82.1489 82, 1489 (2010);
27. B. Deveaud-Plédran, J. Opt. Soc. Am. B JOBPDE 0740-3224 10.1364/JOSAB.29.00A138 29, A138 (2012).
28. M. C. Cross and P. C. Hohenberg, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.65.851 65, 851 (1993).
29. K.-H. Hoffmann and Q. Tang, Ginzburg-Landau Phase Transition Theory and Superconductivity (Birkhäuser, Basel, 2001).
30. I. S. Aranson and L. Kramer, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.74.99 74, 99 (2002);
31. B. A. Malomed, in Encyclopedia of Nonlinear Science, edited by, A. Scott, (Routledge, New York, 2005), p. 157.
32. V. I. Petviashvili and A. M. Sergeev, Dokl. Akad. Nauk SSSR 276, 1380 (1984)
33. V. I. Petviashvili and A. M. Sergeev, [Sov. Phys. Dokl. 29, 493 (1984)].
34. O. Thual and S. Fauve, J. Phys. (Paris) 10.1051/jphys:0198800490110182900 49, 1829 (1988);
35. S. Fauve and O. Thual, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.64.282 64, 282 (1990);
36. W. van Saarloos and P. C. Hohenberg, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.64.749 64, 749 (1990);
37. V. Hakim, P. Jakobsen, and Y. Pomeau, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/11/1/004 11, 19 (1990);
38. B. A. Malomed and A. A. Nepomnyashchy, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.42.6009 42, 6009 (1990);
39. P. Marcq, H. Chaté, and R. Conte, Physica D PDNPDT 0167-2789 10.1016/0167-2789(94)90102-3 73, 305 (1994);
40. N. Akhmediev and V. V. Afanasjev, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.75.2320 75, 2320 (1995);
41. H. R. Brand and R. J. Deissler, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.63.2801 63, 2801 (1989);
42. V. V. Afanasjev, N. Akhmediev, and J. M. Soto-Crespo, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.53.1931 53, 1931 (1996);
43. J. M. Soto-Crespo, N. Akhmediev, and A. Ankiewicz, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.85.2937 85, 2937 (2000);
44. H. Leblond, A. Komarov, M. Salhi, A. Haboucha, and F. Sanchez, J. Opt. A: Pure Appl. Opt. JOAOF8 1464-4258 10.1088/1464-4258/8/3/015 8, 319 (2006); (Pubitemid 43345087)
45. W. H. Renninger, A. Chong, and F. W. Wise, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.77.023814 77, 023814 (2008); (Pubitemid 351393349)
46. J. M. Soto-Crespo, N. Akhmediev, C. Mejia-Cortes, and N. Devine, Opt. Express OPEXFF 1094-4087 10.1364/OE.17.004236 17, 4236 (2009);
47. D. Mihalache, Proc. Rom. Acad. A 11, 142 (2010);
48. Y. J. He, B. A. Malomed, D. Mihalache, F. W. Ye, and B. B. Hu, J. Opt. Soc. Am. B JOBPDE 0740-3224 10.1364/JOSAB.27.001266 27, 1266 (2010);
49. D. Mihalache, Rom. Rep. Phys. 63, 325 (2011);
50. C. Mejia-Cortes, J. M. Soto-Crespo, R. A. Vicencio, and M. I. Molina, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.83.043837 83, 043837 (2011);
51. D. Mihalache, Rom. J. Phys. 57, 352 (2012);
52. O. V. Borovkova, V. E. Lobanov, Y. V. Kartashov, and L. Torner, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.85.023814 85, 023814 (2012).
53. L.-C. Crasovan, B. A. Malomed, and D. Mihalache, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.63.016605 63, 016605 (2000);
54. L.-C. Crasovan, B. A. Malomed, and D. Mihalache, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(01)00571-0 289, 59 (2001); (Pubitemid 32964183)
55. D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, L. Torner, and B. A. Malomed, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.073904 97, 073904 (2006);
56. D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.76.045803 76, 045803 (2007); (Pubitemid 350005075)
57. D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.75.033811 75, 033811 (2007); (Pubitemid 46492684)
58. D. Mihalache and D. Mazilu, Rom. Rep. Phys. 60, 749 (2008).
59. M. Tlidi, M. Haelterman, and P. Mandel, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i1998-00275-y 42, 505 (1998);
60. M. Tlidi and P. Mandel, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.83.4995 83, 4995 (1999);
61. M. Tlidi, J. Opt. B: Quantum Semiclass. Opt. JOBOFD 1464-4266 10.1088/1464-4266/2/3/335 2, 438 (2000).
62. V. Skarka and N. B. Aleksić, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.013903 96, 013903 (2006); (Pubitemid 43248348)
63. N. B. Aleksić, V. Skarka, D. V. Timotijević, and D. Gauthier, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.75.061802 75, 061802 (2007); (Pubitemid 47014654)
64. V. Skarka, D. V. Timotijević, and N. B. Aleksić, J. Opt. A: Pure Appl. Opt. JOAOF8 1464-4258 10.1088/1464-4258/10/7/075102 10, 075102 (2008);
65. V. Skarka, N. B. Aleksić, H. Leblond, B. A. Malomed, and D. Mihalache, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.105.213901 105, 213901 (2010).
66. H. Leblond, B. A. Malomed, and D. Mihalache, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.80.033835 80, 033835 (2009).
67. A. Szameit, J. Burghoff, T. Pertsch, S. Nolte, A. Tünnermann, and F. Lederer, Opt. Express OPEXFF 1094-4087 10.1364/OE.14.006055 14, 6055 (2006).
68. J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature (London) NATUAS 0028-0836 10.1038/nature01452 422, 147 (2003). (Pubitemid 36362743)
69. W. J. Firth and A. J. Scroggie, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.76.1623 76, 1623 (1996).
70. L. A. Lugiato, M. Brambilla, and A. Gatti, Adv. At. Mol. Opt. Phys. 1049-250X 10.1016/S1049-250X(08)60114-7 40, 229 (1999).
71. S. V. Fedorov, A. G. Vladimirov, G. V. Khodova, and N. N. Rosanov, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.61.5814 61, 5814 (2000).
72. D. Mihalache, D. Mazilu, V. Skarka, B. A. Malomed, H. Leblond, N. B. Aleksić, and F. Lederer, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.82.023813 82, 023813 (2010).
73. D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.81.025801 81, 025801 (2010).
74. L. Bergé, Phys. Rep. 0370-1573 10.1016/S0370-1573(97)00092-6 303, 259 (1998).
75. M. Desaix, D. Anderson, and M. Lisak, J. Opt. Soc. Am. B JOBPDE 0740-3224 10.1364/JOSAB.8.002082 8, 2082 (1991).
76. B. A. Malomed, Physica D PDNPDT 0167-2789 10.1016/0167-2789(87)90052-2 29, 155 (1987).
77. H. Sakaguchi, Physica D PDNPDT 0167-2789 10.1016/j.physd.2005.07.011 210, 138 (2005). (Pubitemid 41277027)
78. Y. Kominis, S. Droulias, P. Papagiannis, and K. Hizanidis, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.85.063801 85, 063801 (2012).
79. A. V. Ustinov, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(89)90196- 5 136, 155 (1989);
80. B. A. Malomed, Phys. Rev. B 1098-0121 10.1103/PhysRevB.41.2616 41, 2616 (1990);
81. A. Shnirman, Z. Hermon, A. V. Ustinov, B. A. Malomed, and E. Ben-Jacob, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.50.12793 50, 12793 (1994).
82. D. Novoa, B. A. Malomed, H. Michinel, and V. M. Pérez- García, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.101.144101 101, 144101 (2008).
83. A. G. Vladimirov, D. V. Skryabin, G. Kozyreff, P. Mandel, and M. Tlidi, Opt. Express OPEXFF 1094-4087 10.1364/OPEX.14.000001 14, 1 (2006). (Pubitemid 43064027)