Random Attractors for the Dissipative Hamiltonian Amplitude Equation Governing Modulated Wave Instabilities with Additive Noise

摘要

In this paper, we study the random dynamical system (RDS) generated by the dissipative Hamiltonian amplitude equation with additive noise defined on the periodic boundaries. We investigate the existence of a compact random attractor for the RDS associated with the equation through introducing two functions and one process in E0=H1×L2. The compactness of the RDS is established by the decomposition of solution semigroup.