Article
The Complex Cubic-Quintic Ginzburg-Landau Equation: Hopf Bifurcations Yielding Traveling Waves
Mathematics and Computers in Simulation
(2007)
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.
Disciplines
Publication Date
March 30, 2007
DOI
https://doi.org/10.1016/j.matcom.2006.10.022
Citation Information
S.C. Mancas and S. Roy Choudhury. "The Complex Cubic-Quintic Ginzburg-Landau Equation: Hopf Bifurcations Yielding Traveling Waves" Mathematics and Computers in Simulation Vol. 74 Iss. 4-5 (2007) p. 281 - 291 Available at: http://works.bepress.com/stefani_mancas/124/