Traveling hole solutions to the complex Ginzburg-Landau equation as perturbations of nonlinear Schrödinger dark solitons

Physica D: Nonlinear Phenomena

Volumn 102, Issue 3-4, 1997, Pages 234-252

  Lega, Joceline ^a   Fauve, Stephan ^b  

^a INSTITUT NON LINÉAIRE DE NICE   (France)

^b UNIVERSITÉ DE LYON   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000902465     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(96)00218-7     Document Type: Article

References (28)

1. Y. Kuramoto, Chemical Oscillations, Waves and Turbulence, Springer Series in Synergetics, Vol. 19 (Springer, Berlin, 1984).
2. P. Coullet, L. Gil and F. Rocca, Opt. Comm. 73 (1989) 403.
3. A.C. Newell and J.V. Moloney, Nonlinear Optics (Addison-Wesley, Redwood City, CA, 1992).
4. P.A. Bélanger, L. Gagnon and C. Paré, Solitary pulses in an amplified nonlinear dispersive medium, Opt. Lett. 14 (1989) 943.
5. Y. Kuramoto and T. Tsuzuki, Persistent propagation of concentration waves in dissipative media far from thermal equilibrium, Prog. Theor. Phys. 55 (1976) 356.
6. Y. Pomeau and P. Manneville, Stability and fluctuations of a spatially periodic convective flow, J. Phys. (Paris) Lett. 40 (1979) 609.
7. P. Coullet, L. Gil and J. Lega, Defect-mediated turbulence, Phys. Rev. Lett. 62 (1989) 1619;
8. A form of turbulence associated with defects, Physica D 37 (1989) 91.
9. L. Gil, Space and time intermittency behaviour of a 1-d complex Ginzburg-Landau equation, Nonlinearity 4 (1991) 1213.
10. B.A. Schraiman, A. Pumir, W. van Saarloos, P.C. Hohenberg, H. Chaté and M. Holen, Physica D 57 (1992) 241.
11. H. Chaté, Spatio-temporal intermittency regimes of the one-dimensional complex Ginzburg-Landau equation, Nonlinearity 7 (1994) 185.
12. F. Daviaud, J. Lega, P. Bergé, P. Coullet and M. Dubois, Spatio-temporal intermittency in a 1-d convective pattern: Theoretical model and experiments, Physica D 55 (1992) 287.
13. J. Lega, S. Jucquois, B. Janiaud and V. Croquette, Localized phase jumps in wave trains, Phys. Rev. A 45 (1992) 5596.
14. N. Bekki and K. Nozaki, Phys. Lett. A 110 (1985) 133.
15. R. Hirota, Direct method of finding exact solutions of nonlinear evolution equations, in: Bäcklund Transformations, ed. R.M. Miura, Lecture Notes in Mathematics, Vol. 515 (Springer, Berlin, 1976).
16. H. Sakaguchi, Prog. Theor. Phys. 85 (1991) 417.
17. H. Chaté and P. Manneville, Phys. Lett. A 171 (1992) 183.
18. S. Sasa and T. Iwamoto, Phys. Lett. A 175 (1993) 289.
19. S. Popp, O. Stiller, I. Aranson and L. Kramer, Hole solutions in the ID complex Ginzburg-Landau equation, Physica D 84 (1995) 398.
20. S. Popp, O. Stiller, I. Aranson, A. Weber and L. Kramer, Phys. Rev. Lett. 70 (1993) 3880.
21. A. Doelman, Breaking the hidden symmetry in the Ginzburg-Landau equation, Physica D 97 (1996) 398.
22. W. van Saarloos and P.C. Hohenberg, Fronts, pulses, sources and sinks in generalized complex Ginzburg-Landau equations, Physica D 56 (1992) 303.
23. C. Elphick and E. Meron, Localized structures in surface waves, Phys. Rev. A 40 (1989) 3226.
24. Y.S. Kivshar and Y. Xiaoping, Perturbation-induced dynamics of dark solitons, Phys. Rev. E 49 (1994) 1657 and references therein.
25. V.V. Konotop and V.E. Vekslerchick, Phys. Rev. E 49 (1994) 2397 and references therein.
26. O. Stiller, S. Popp and L. Kramer, From dark solitons in the defocusiong nonlinear Schrödinger to holes in the complex Ginzburg-Landau equation, Physica D 84 (1995) 424.
27. A. Hasegawa and F. Tappert, Appl. Phys. Lett. 23 (1973) 171.
28. V.E. Zakharov and A.B. Shabat, Sov. Phys. JETP 37 (1973) 823.