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

    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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