Time-periodic solitons in a damped-driven nonlinear Schrödinger equation

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

Volumn 83, Issue 5, 2011, Pages

  Barashenkov, I V ^a   Zemlyanaya, E V ^b   Van Heerden, T C ^c,d  

^a UNIVERSITY OF CAPE TOWN   (South Africa)

^b National Institute for Theoretical Physics   (South Africa)

^c JOINT INSTITUTE FOR NUCLEAR RESEARCH   (Russian Federation)

^d UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION DIAGRAM; DINGER EQUATION; HOMOCLINIC BIFURCATIONS; PERIODIC-SOLITON; RADIATION FREQUENCIES; SPATIOTEMPORAL DOMAIN;

BIFURCATION (MATHEMATICS);

SOLITONS;

EID: 79961090432     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.83.056609     Document Type: Article

References (50)

1. J. W. Miles, J. Fluid Mech. JFLSA7 0022-1120 10.1017/S0022112084002433 148, 451 (1984).
2. E. W. Laedke and K. H. Spatschek, J. Fluid Mech. JFLSA7 0022-1120 10.1017/S0022112091001568 223, 589 (1991).
3. C. Elphick and E. Meron, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.40.3226 40, 3226 (1989);
4. X. N. Chen and R. J. Wei, J. Fluid Mech. JFLSA7 0022-1120 10.1017/S0022112094000145 259, 291 (1994);
5. W. Zhang and J. Viñals, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.74.690 74, 690 (1995);
6. A. D. D. Craik and J. G. M. Armitage, Fluid Dyn. Res. FDRSEH 0169-5983 10.1016/0169-5983(94)00037-Z 15, 129 (1995);
7. S. P. Decent and A. D. D. Craik, J. Fluid Mech. JFLSA7 0022-1120 10.1017/S0022112095001704 293, 237 (1995);
8. W.A.Wang, X. Wang, J. Wang, and R. Wei, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(96)00406-9 219, 74 (1996);
9. S. P. Decent, Fluid Dyn. Res. FDRSEH 0169-5983 10.1016/S0169-5983(96) 00063-9 21, 115 (1997); (Pubitemid 27416656)
10. X. Wang and R. Wei, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.78.2744 78, 2744 (1997);
11. X. Wang and R. Wei, Phys. Rev. E PRLTAO 1539-3755 10.1103/PhysRevE.57. 2405 57, 2405 (1998);
12. G. Miao and R. Wei, Phys. Rev. E PRLTAO 1539-3755 10.1103/PhysRevE.59. 4075 59, 4075 (1999);
13. W. Chen, L.A.Lu, and Y. Zhu, Phys. Rev. E PRLTAO 1539-3755 10.1103/PhysRevE.71.036622 71, 036622 (2005); (Pubitemid 40619891)
14. L. Zhang, X. Wang, and Z. Tao, ibid. PRLTAO 1539-3755 10.1103/PhysRevE.75.036602 75, 036602 (2007). (Pubitemid 46393406)
15. D. Astruc and S. Fauve, in IUTAM Symposium on Free Surface Flows: Proceedings of the IUTAM Symposium Held in Birmingham, UK, 10-14 July 2000, edited by, A. C. King, and, Y. D. Shikhmurzaev, Fluid Mechanics and Its Applications, Vol. 62 (Kluwer, Dordrecht, 2001);
16. I. V. Barashenkov, N. V. Alexeeva, and E. V. Zemlyanaya, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.89.104101 89, 104101 (2002).
17. M. G. Clerc, S. Coulibaly, and D. Laroze, Phys. Rev. E PRLTAO 1539-3755 10.1103/PhysRevE.77.056209 77, 056209 (2008); (Pubitemid 351718036)
18. M. G. Clerc, S. Coulibaly, and D. Laroze, Int. J. Bifurcation and Chaos IJBEE4 0218-1274 10.1142/S0218127409024438 19, 2717 (2009);
19. M. G. Clerc, S. Coulibaly, and D. Laroze, Int. J. Bifurcation and Chaos IJBEE4 0218-1274 10.1142/S0218127409024967 19, 3525 (2009).
20. B. Denardo, B. Galvin, A. Greenfield, A. Larraza, S. Putterman, and W. Wright, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.68.1730 68, 1730 (1992);
21. W.-Z. Chen, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.49.15063 49, 15063 (1994);
22. G. Huang, S.-Y. Lou, and M. Velarde, Int. J. Bifurcation and Chaos IJBEE4 0218-1274 10.1142/S0218127496001119 6, 1775 (1996); (Pubitemid 126310069)
23. N. V. Alexeeva, I. V. Barashenkov, and G. P. Tsironis, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.84.3053 84, 3053 (2000);
24. W. Chen, B. Hu, and H. Zhang, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.65.134302 65, 134302 (2002);
25. H.-Q. Xu and Y. Tang, Chin. Phys. Lett. CPLEEU 0256-307X 10.1088/0256-307X/23/6/052 23, 1544 (2006); (Pubitemid 44159560)
26. J. Cuevas, L. Q. English, P. G. Kevrekidis, and M. Anderson, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.102.224101 102, 224101 (2009).
27. I. H. Deutsch and I. Abram, J. Opt. Soc. Am. B JOBPDE 0740-3224 10.1364/JOSAB.11.002303 11, 2303 (1994);
28. A. Mecozzi, L. Kath, P. Kumar, and C. G. Goedde, Opt. Lett. OPLEDP 0146-9592 10.1364/OL.19.002050 19, 2050 (1994);
29. S. Longhi, Opt. Lett. OPLEDP 0146-9592 10.1364/OL.20.000695 20, 695 (1995);
30. V. J. Sánchez-Morcillo, I. Pérez-Arjona, F. Silva, G. J. de Valcárcel, and E. Roldán, Opt. Lett. OPLEDP 0146-9592 10.1364/OL.25.000957 25, 957 (2000).
31. I. V. Barashenkov, M. M. Bogdan, and V. I. Korobov, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/15/2/001 15, 113 (1991).
32. M. G. Clerc, S. Coulibaly, and D. Laroze, Physica D PDNPDT 0167-2789 10.1016/j.physd.2009.10.008 239, 72 (2009);
33. M. G. Clerc, S. Coulibaly, and D. Laroze, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/90/38005 90, 38005 (2010).
34. T.-C. Jo and D. Armbruster, Phys. Rev. E EULEEJ 1539-3755 10.1103/PhysRevE.68.016213 68, 016213 (2003).
35. See also the following references where the parametrically driven cubic Klein-Gordon equation is studied in Fourier space: W. I. Newman, R. H. Rand, and A. L. Newman, Chaos CHAOEH 1054-1500 10.1063/1.166397 9, 242 (1999);
36. T. Bakri, H. G. E. Meijer, and F. Verhulst, J. Nonlinear Sci. JNSCEK 0938-8974 10.1007/s00332-009-9045-2 19, 571 (2009).
37. I. V. Barashenkov and E. V. Zemlyanaya, Phys. Rev. E EULEEJ 1539-3755 10.1103/PhysRevE.83.056610 83, 056610 (2011).
38. M. Bondila, I. V. Barashenkov, and M. M. Bogdan, Physica D PDNPDT 0167-2789 10.1016/0167-2789(95)00126-O 87, 314 (1995).
39. N. V. Alexeeva, I. V. Barashenkov, and D. E. Pelinovsky, Nonlinearity NONLE5 0951-7715 10.1088/0951-7715/12/1/007 12, 103 (1999).
40. H. Friedel, E. W. Laedke, and K. H. Spatschek, J. Fluid Mech. JFLSA7 0022-1120 10.1017/S0022112095000383 284, 341 (1995).
41. E. V. Zemlyanaya and I. V. Barashenkov, Math. Modelling 16, 3 (2004).
42. V. I. Arnold, Mathematical Methods of Classical Mechanics, Graduate Texts in Mathematics (Springer Verlag, New York, 2010).
43. D. M. Ambrose and J. Wilkening, Commun. Appl. Math. Comput. Sci. JFLSA7 1559-3940 10.2140/camcos.2009.4.177 4, 177 (2009);
44. D. M. Ambrose and J. Wilkening, J. Nonlinear Sci. JNSCEK 0938-8974 10.1007/s00332-009-9058-x 20, 277 (2010).
45. L. P. Shil'nikov, Dokl. Akad. Nauk SSSR 160, 558 (1965).
46. L. P. Shil'nikov, Mat. Sbornik 81, 92 (1970).
47. P. Glendinning and C. Sparrow, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF01010828 35, 645 (1984).
48. C. Sparrow, The Lorenz Equations: Bifurcations, Chaos and Strange Attractors, Applied Mathematical Sciences 41 (Springer-Verlag, New York, 1982).
49. D. R. Moore, J. Toomre, E. Knobloch, and N. O. Weiss, Nature (London) NATUAS 0028-0836 10.1038/303663a0 303, 663 (1983);
50. E. Knobloch, D. R. Moore, J. Toomre, and N. O. Weiss, J. Fluid Mech. JFLSA7 0022-1120 10.1017/S0022112086000216 166, 409 (1986).