Some stability results for the complex Ginzburg–Landau equation

Abstract

Using some classical methods of dynamical systems, stability results and asymptotic decay of strong solutions for the complex Ginzburg–Landau equation (CGL), [Formula: see text] with [Formula: see text], are obtained. Moreover, we show the existence of bound-states under certain conditions on the parameters and on the domain. We conclude with the proof of asymptotic stability of these bound-states when [Formula: see text] and [Formula: see text] large enough.