Stationary modulated-amplitude waves in the 1-D complex Ginzburg-Landau equation
arXiv:nlin/0208001
Abstract
We reformulate the one-dimensional complex Ginzburg-Landau equation as a fourth order ordinary differential equation in order to find stationary spatially-periodic solutions. Using this formalism, we prove the existence and stability of stationary modulated-amplitude wave solutions. Approximate analytic expressions and a comparison with numerics are given.
29 pages, 4 figures