Asymptotic compactness of stochastic complex Ginzburg-Landau equation on an unbounded domain

The Ginzburg-Landau-type complex equations are simplified mathematical models for various pattern formation systems in mechanics, physics, and chemistry. In this paper, we show that the complex Ginzburg-Landau equations on the whole real line perturbed by an additive space-time white noise generates an asymptotically compact stochastic or random dynamical system in weighted L2-spaces