Title

The complex cubic-quintic Ginzburg-Landau equation: Hopf bifurcations yielding traveling waves

Authors

Authors

S. C. Mancas;S. R. Choudhury

Comments

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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

WOS:000245216500003

ISSN

0378-4754

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