Localized states in a triangular set of linearly coupled complex Ginzburg-Landau equations

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

Volumn 74, Issue 6, 2006, Pages

  Sigler, Ariel ^a   Malomed, Boris A ^a   Skryabin, Dmitry V ^b  

^a TEL AVIV UNIVERSITY   (Israel)

^b University of Bath   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

FIBER LASERS; LINEAR EQUATIONS; SYSTEM STABILITY; VORTEX FLOW;

GINZBURG-LANDAU EQUATIONS; LOCALIZED STATES; PATTERN-FORMATION MODEL; TRIANGULAR CONFIGURATION;

QUANTUM THEORY;

EID: 33845524281     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.74.066604     Document Type: Article

References (41)

1. I. S. Aranson and L. Kramer, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.74.99 74, 99 (2002);
2. Dissipative Solitons, edited by, N. Akhmediev, and, A. Ankiewicz, (Springer, Berlin, Heidelberg, 2005).
3. B. A. Malomed, in Encyclopedia of Nonlinear Science, edited by, A. Scott, (Routledge, New York, 2005), p. 157.
4. F. T. Arecchi, S. Boccaletti, and P. Ramazza, Phys. Rep. PRPLCM 0370-1573 10.1016/S0370-1573(99)00007-1 318, 1 (1999);
5. M. Ipsen, L. Kramer, and P. G. Sorensen, Phys. Rep. PRPLCM 0370-1573 10.1016/S0370-1573(00)00062-4 337, 193 (2000);
6. P. Mandel and M. Tlidi, J. Opt. B: Quantum Semiclassical Opt. JOBOFD 1464-4266 10.1088/1464-4266/6/9/R02 6, R60 (2004).
7. F. O. Ilday and F. W. Wise, J. Opt. Soc. Am. B JOBPDE 0740-3224 19, 470 (2000);
8. Y. D. Gong, P. Shum, D. Y. Tang, C. Lu, X. Guo, V. Paulose, W. S. Man, and H. Y. Tam, Opt. Laser Technol. OLTCAS 0030-3992 10.1016/j.optlastec.2003.09. 013 36, 299 (2004).
9. L. M. Hocking and K. Stewartson, Proc. R. Soc. London, Ser. A PRLAAZ 1364-5021 326, 289 (1972);
10. N. R. Pereira and L. Stenflo, Phys. Fluids PFLDAS 0031-9171 20, 1733 (1977).
11. A. J. Scroggie, W. J. Firth, G. S. McDonald, M. Tlidi, R. Lefever, and L. A. Lugiato, Chaos, Solitons Fractals CSFOEH 0960-0779 10.1016/0960-0779(94) 90084-1 4, 1323 (1994).
12. V. I. Petviashvili and A. M. Sergeev, Dokl. Akad. Nauk SSSR DANKAS 0002-3264 276, 1380 (1984)
13. V. I. Petviashvili and A. M. Sergeev, [Sov. Phys. Dokl. SPHDA9 0038-5689 29, 493 (1984)].
14. B. A. Malomed, Physica D PDNPDT 0167-2789 10.1016/0167-2789(87)90052-2 29, 155 (1987).
15. O. Thual and S. Fauve, J. Phys. (Paris) JOPQAG 0302-0738 49, 1829 (1988);
16. S. Fauve and O. Thual, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.64.282 64, 282 (1990);
17. W. van Saarloos and P. C. Hohenberg, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.64.749 64, 749 (1990);
18. B. A. Malomed and A. A. Nepomnyashchy, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.42.6009 42, 6009 (1990);
19. V. Hakim, P. Jakobsen, and Y. Pomeau, Europhys. Lett. EULEEJ 0295-5075 11, 19 (1990);
20. P. Marcq, H. Chaté, and R. Conte, Physica D PDNPDT 0167-2789 10.1016/0167-2789(94)90102-3 73, 305 (1994);
21. J. M. Soto-Crespo, N. N. Akhmediev, and V. V. Afanasjev, J. Opt. Soc. Am. B JOBPDE 0740-3224 13, 1439 (1996);
22. O. Descalzi, M. Argentina, and E. Tirapegui, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.67.015601 67, 015601 (R) (2003).
23. H. Sakaguchi, Physica D PDNPDT 0167-2789 210, 138 (2005).
24. B. A. Malomed and H. G. Winful, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.53.5365 53, 5365 (1996);
25. J. Atai and B. A. Malomed, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.54.4371 54, 4371 (1996).
26. J. Atai and B. A. Malomed, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(98)00505-2 246, 412 (1998).
27. H. Sakaguchi and B. A. Malomed, Physica D PDNPDT 0167-2789 10.1016/S0167-2789(00)00176-7 147, 273 (2000);
28. H. Sakaguchi and B. A. Malomed, Physica D PDNPDT 0167-2789 10.1016/S0167-2789(01)00243-3 154, 229 (2001).
29. D. T. Walton and H. G. Winful, Opt. Lett. OPLEDP 0146-9592 10.1038/366720a0 18, 720 (1993);
30. E. Marti-Panameno, L. C. Gomez-Pavon, A. Luis-Ramos, M. M. Mendez-Otero, and M. D. I. Castillo, Opt. Commun. OPCOB8 0030-4018 10.1016/S0030-4018(01) 01275-5 194, 409 (2001).
31. H. Sakaguchi, Prog. Theor. Phys. PTPKAV 0033-068X 10.1143/PTP.93.491 93, 491 (1995);
32. H. Sakaguchi, Prog. Theor. Phys. PTPKAV 0033-068X 10.1143/PTP.95.823 95, 823 (1996).
33. A. Sigler and B. A. Malomed, Physica D PDNPDT 0167-2789 212, 305 (2005).
34. L. Li, A. Schülzgen, S. Chen, V. L. Temyanko, J. V. Moloney, and N. Peyghambarian, Opt. Lett. OPLEDP 0146-9592 10.1364/OL.31.002577 31, 2577 (2006);
35. L. Michaille, C. R. Bennett, D. M. Taylor, T. J. Shepherd, J. Broeng, H. R. Simonsen, and A. Petersson, Opt. Lett. OPLEDP 0146-9592 10.1364/OL.30.001668 30, 1668 (2005).
36. D. V. Skryabin and A. G. Vladimirov, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.89.044101 89, 044101 (2002).
37. 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);
38. 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 19, 369 (2002);
39. K. Ogusu, J. Yamasaki, S. Maeda, M. Kitao, and M. Minakata, Opt. Lett. OPLEDP 0146-9592 10.1364/OL.29.000265 29, 265 (2004).
40. A. V. Buryak and A. A. Akhmediev, J. Opt. Soc. Am. B JOBPDE 0740-3224 11, 804 (1994).
41. A. Gubeskys and B. A. Malomed, Eur. Phys. J. D EPJDF6 1434-6060 10.1140/epjd/e2003-00304-5 28, 283 (2004).