On the nonlinear stability of plane waves for the ginzburg-landau equation

Abstract

I consider the nonlinear stability of plane wave solutions to a Ginzburg-Landau equation with additional fifth-order terms and cubic terms containing spatial derivatives. I show that, under the constraint that the diffusion coefficient be real, these waves are stable. Furthermore, it is shown that the radial component of the perturbation decays at a faster rate than the phase component of the perturbation as t → ∞. The result is also applicable to the classical Ginzburg-Landau equation. © 1994 John Wiley & Sons, Inc.