Attractor for the nonlinear Schrödinger equation with a nonlocal nonlinear term

Abstract

In this paper, we consider the long-time behavior of solutions of the dissipative 1D nonlinear Schrodinger (NLS) equation with nonlocal integral term and with periodic boundary conditions. We prove the existence of the global attractor $ \mathcal{A} $ for the nonlocal equation in the strong topology of H 1(?). We also prove that the global attractor is regular, i.e., $ \mathcal{A} \subset {H^2}\left( \Omega \right) $ , assuming that f(x) is of class C 2. Furthermore, we estimate the number of the determining modes for this equation.