Submitting Campus

Daytona Beach

Department

Department of Mathematics

Document Type

Article

Publication/Presentation Date

5-2006

Abstract/Description

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.

Publication Title

Chaos, Solitons & Fractals

DOI

https://doi.org/10.1016/j.chaos.2005.08.080

Publisher

Elsevier

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