Sources and sinks in the vicinity of a weakly inverted instability

International Journal of Bifurcation and Chaos

Volumn 17, Issue 8, 2007, Pages 2821-2826

  Cisternas, Jaime ^a   Descalzi, Orazio ^a  

^a UNIVERSIDAD DE LOS ANDES   (Chile)

Author keywords

Cubic quintic Ginzburg Landau equation; Dissipative dark solitons; Sinks; Sources

Indexed keywords

ASYMPTOTIC ANALYSIS; COMPUTER SIMULATION; PERTURBATION TECHNIQUES; SOLITONS; WAVE PROPAGATION;

ASYMPTOTIC VALUES; CUBIC-QUINTIC GINZBURG-LANDAU EQUATIONS; SINKS; TRAVELING WAVES (TW);

SYSTEM STABILITY;

EID: 34748918858     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127407018804     Document Type: Article

References (15)

1. Afanasjev, V. V., Akhmediev, N. & Soto-Crespo, J. M. [1996] "Three forms of localized solutions of the quintic complex Ginzburg-Landau equation," Phys. Rev. E 53, 1931-1939.
2. Aranson, I. & Kramer, L. [2002] "The world of the complex Ginzburg-Landau equation," Rev. Mod. Phys. 74, 99-143.
3. Brand, H. R. & Deissler, R. J. [1989] "Interaction of localized solutions for subcritical bifurcations," Phys. Rev. Lett. 63, 2801-2804.
4. Burguete, J., Chaté, H., Daviaud, F. & Mukolobwiez, N. [1999] "Bekki-Nozaki amplitude holes in hydrothermal nonlinear waves," Phys. Rev. Lett. 82, 3252-3255.
5. Deissler, R. J. & Brand, H. R. [1994] "Periodic, quasiperiodic, and chaotic localized solutions of the quintic complex Ginzburg-Landau equation," Phys. Rev. Lett. 72, 478-481.
6. Descalzi, O. & Brand, H. R. [2005] "Stable stationary and breathing holes at the onset of a weakly inverted instability," Phys. Rev. E 72, 055202-1(R)-055202-4(R).
7. Descalzi, O., Gutiérrez, P. & Tirapegui, E. [2005] "Localized structures in nonequilibrium systems," Int. J. Mod. Phys. C 16, 1909-1916.
8. Eckart, C. [1948] "The approximate solution of one-dimensional wave equations," Rev. Mod. Phys. 20, 399-417.
9. Komarov, A., Leblond, H. & Sanchez, F. [2005] "Quintic complex Ginzburg-Landau model for ring fiber lasers," Phys. Rev. E 72, 025604-1(R)-025604-4(R).
10. Nozaki, K. & Bekki, N. [1984] "Exact solutions of the generalized Ginzburg-Landau equation," J. Phys. Soc. Jpn. 53, 1581-1582.
11. Remoissenet, M. [1999] Waves called Solitons (Springer-Verlag, Berlin).
12. Sakaguchi, H. [1991] "Hole solutions in the complex Ginzburg-Lanau equation near a subcritical bifurcation," Prog. Theor. Phys. 86, 7-12.
13. Thual, O. & Fauve, S. [1988] "Localized structures generated by subcritical instabilities," J. Phys. France 49, 1829-1833.
14. van Saarloos, W. & Hohenberg, P. C. [1990] "Puises and fronts in the complex Ginzburg-Landau equation near a subcritical bifurcation," Phys. Rev. Lett. 64, 749-752.
15. Zabusky, N. J. & Kruskal, M. D. [1965] "Interaction of solitons in a collisionless plasma and the recurrence of initial states," Phys. Rev. Lett. 15, 240-243.