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.
Original language | American English |
---|---|
Journal | Chaos, Solitons Fractals |
Volume | 28 |
DOIs | |
State | Published - May 1 2006 |
Keywords
- cubic-quintic Ginzburg-Landau equation
- traveling wave reduction
- Hopf bifurcations
Disciplines
- Applied Mathematics
- Physical Sciences and Mathematics