The complex cubic-quintic Ginzburg-Landau equation: Hopf bifurcations yielding traveling waves
Abbreviated Journal Title
Math. Comput. Simul.
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
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.
Mathematics and Computers in Simulation
Article; Proceedings Paper
"The complex cubic-quintic Ginzburg-Landau equation: Hopf bifurcations yielding traveling waves" (2007). Faculty Bibliography 2000s. 7397.