Traveling wavetrains in the complex cubic-quintic Ginzburg-Landau equation

Chaos, Solitons and Fractals

Volumn 28, Issue 3, 2006, Pages 834-843

  Mancas, Stefan C ^a   Choudhury, S Roy ^a  

^a UNIVERSITY OF CENTRAL FLORIDA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; PERTURBATION TECHNIQUES; WAVE EFFECTS;

CUBIC-QUINTIC GINZBURG-LANDAU EQUATION; HOMOCLINIC ORBITS; PERIODIC ORBITS; TRAVELING WAVETRAINS;

BIFURCATION (MATHEMATICS);

EID: 27644577260     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2005.08.080     Document Type: Article

References (33)

1. Akhmediev N. Pulsating solitons in dissipative systems. In: 4th IMACS Conf. on Nonlinear Waves, Athens, Georgia, April 2005.
2. N. Akhmediev, J. Soto-Crespo, and G. Town Pulsating solitons, chaotic solitons, period doubling, and pulse coexistence in mode-locked laser: CGLE approach Phys Rev E 63 2001 56602
3. R. Alvarez, M. van Hecke, and W. van Saarloos Sources and sinks separating domains of left- and right-traveling waves: experiment versus amplitude equations Phys Rev E 56 1997 R1306
4. I.S. Aranson, and L. Kramer The world of the complex Ginzburg-Landau equation Rev Mod Phys 74 2002 99
5. V.I. Arnold Lectures on bifurcations in versal families Russ Math Surv 27 1972 54
6. D. Artigas, L. Torner, and N. Akhmediev Robust heteroclinic cycles in the one-dimension CGLE Opt Commun 143 1997 322
7. N.J. Balmforth Solitary waves and homoclinic orbits Ann Rev Fluid Mech 27 1995 335
8. L. Brusch, A. Torcini, and M. Bär Nonlinear analysis of the Eckhaus instability: modulated amplitude waves and phase chaos Phys D 160 2001 127
9. L. Brusch, A. Torcini, M. van Hecke, M.G. Zimmermann, and M. Bär Modulated amplitude waves and defect formation in the one-dimensional complex Ginzburg-Landau equation Phys D 160 2001 127
10. C. Bowman, and A.C. Newell Natural patterns and wavelets Rev Mod Phys 70 1998 289
11. R.K. Dodd, J.C. Eilbeck, J.D. Gibbon, and H.C. Morris Solitons and nonlinear wave equations 1982 Academic London
12. A. Doelman Slow time-periodic solutions of the GL equation Phys D 40 1989 156
13. A. Doelman Periodic and quasiperiodic solutions of degenerate modulation equations Phys D 53 1991 249
14. A. Doelman Traveling waves in the complex GL equation J Nonlinear Sci 3 1993 225
15. P.G. Drazin, and R.S. Johnson Solitons: an introduction 1989 Cambridge University Press Cambridge
16. P.G. Drazin, and W.H. Reid Hydrodynamic stability 1981 Cambridge University Press Cambridge
17. J. Duan, and P. Holmes Fronts, domain walls and pulses in a generalized GL equation Proc Edin Math Soc 38 1995 77
18. M. Golubitski, and D.G. Schaffer Singularities and groups in bifurcation theory vol. 51 1985 Springer New York
19. J. Guckenhemer, and P. Holmes Nonlinear oscillations, dynamical systems, and bifurcations of vector fields vol. 42 1983 Springer-Verlag New York
20. P. Holmes Spatial structure of time periodic solutions of the GL equation Phys D 23 1986 84
21. L.R. Keefe Dynamics of perturbed wavetrain solutions to the Ginzburg-Landau equation Stud Appl Math 73 1985 91
22. M.J. Landman Solutions of the GL equation of interest in shear flow Stud Appl Math 76 1987 187
23. W.F. Langford Periodic and steady-state mode interactions lead to tori SIAM J Appl Math 37 1979 22
24. J.D. Murray Mathematical biology 1989 Springer-Verlag Berlin
25. P.K. Newton, and L. Sirovich Instabilities of the Ginzburg-Landau equation: periodic solutions Quart Appl Math XLIV 1984 49
26. P.K. Newton, and L. Sirovich Instabilities of the Ginzburg-Landau equation pt. II: secondary bifurcations Quart Appl Math XLIV 1986 367
27. L.M. Pismen Dynamics of lumped chemically reacting systems near singular bifurcations points Chem Eng Sci 39 1984 1063
28. L.M. Pismen Dynamics of lumped chemically reacting systems near singular bifurcations points-II. Almost Hamiltonian dynamics Chem Eng Sci 40 1985 905
29. Planeaux J. Bifurcation phenomena in CSTR dynamics. PhD thesis, University of Minnesota, 1993.
30. J. Satsuma, and N. Yajima Initial-value problems of one-dimensional self-modulation of nonlinear-waves in dispersive media Prog Theoret Phys Suppl 55 1974 284
31. J.M. Soto-Crespo, N. Akhmediev, and G. Town Interrelation between various branches of stable solitons in dissipative systems Opt Commun 199 2001 283
32. M. van Hecke, C. Storm, and W. van Saarloos Sources, sinks and wavenumber selection in coupled CGL equations Phys D 134 1999 1
33. W. van Saarloos, and P.C. Hohenberg Fronts, pulses, sources and sinks in generalized complex Ginzburg-Landau equation Phys D 56 1992 303