Traveling Wavetrains in the Complex Cubic-Quintic Ginzburg-Landau Equation
arXiv:1305.1191 · doi:10.1016/j.chaos.2005.08.080
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.
11 pages, 1 figure. Redone the references. arXiv admin note: substantial text overlap with arXiv:1301.5222, arXiv:1301.5350