Global Attractor for a Class of Coupled Nonlinear Schrödinger Equations

Abstract

In this paper, the long time behavior of solution for a class of coupled nonlinear Schrodinger equation with zero order dissipation is studied. We first construct the global weak attractor for this system in H2 per(?) H2 per(?). And then by exact analysis of the energy equation, we shown that the global weak attractor is actually the global strong attractor in H2 per(?) H2 per(?). We also estimate the uniform Lyapunov exponents on the attractor, which allows us to prove its finite dimensional property.