Traveling Wavetrains in the Complex Cubic-Quintic Ginzburg-Landau Equation
Stefan C. Mancas, S. Roy Choudhury
TL;DR
This paper investigates periodic solutions and their stability in the complex cubic-quintic Ginzburg-Landau equation using bifurcation and perturbation theories, revealing global structures like homoclinic orbits.
Contribution
It provides explicit results for post-bifurcation periodic orbits and their stability, and explores global bifurcation structures in the equation.
Findings
Explicit periodic solutions and stability results
Analysis of Hopf bifurcations and global structures
Consideration of degenerate bifurcations and homoclinic orbits
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.
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