Title

The Complex Cubic-Quintic Ginzburg-Landau Equation: Hopf Bifurcations Yielding Traveling Waves

Keywords

CGLE; Hopf bifurcations; Periodic; Wavetrains

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. © 2006 IMACS.

Publication Date

3-30-2007

Publication Title

Mathematics and Computers in Simulation

Volume

74

Issue

4-5

Number of Pages

281-291

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.matcom.2006.10.022

Socpus ID

33847159138 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/33847159138

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