Title
The complex cubic-quintic Ginzburg-Landau equation: Hopf bifurcations yielding traveling waves
Abbreviated Journal Title
Math. Comput. Simul.
Keywords
periodic; wavetrains; Hopf bifurcations; CGLE; CHEMICALLY REACTING SYSTEMS; MODULATED AMPLITUDE WAVES; TIME-PERIODIC; SOLUTIONS; DYNAMICS; SOLITONS; FRONTS; POINTS; PULSES; SINKS; Computer Science, Interdisciplinary Applications; Computer Science, ; Software Engineering; Mathematics, Applied
Abstract
In this paper we use a traveling wave reduction or a so-called spatial approximation to comprehensively investigate the periodic solutions of the complex cubic-quintic Ginzburg-Landau equation. The primary tools used here are Hopf bifurcation theory and perturbation theory. Explicit results are obtained for the post-bifurcation periodic orbits and their stability. Generalized and degenerate Hopf bifurcations are also briefly considered to track the emergence of global structure such as homoclinic orbits. (c) 2006 IMACS. Published by Elsevier B.V All rights reserved.
Journal Title
Mathematics and Computers in Simulation
Volume
74
Issue/Number
4-5
Publication Date
1-1-2007
Document Type
Article; Proceedings Paper
Language
English
First Page
281
Last Page
291
WOS Identifier
ISSN
0378-4754
Recommended Citation
"The complex cubic-quintic Ginzburg-Landau equation: Hopf bifurcations yielding traveling waves" (2007). Faculty Bibliography 2000s. 7397.
https://stars.library.ucf.edu/facultybib2000/7397
Comments
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