Long-Time Behavior of Finite Difference Solutions of Three-Dimensional Nonlinear Schrödinger Equation with Weakly Damped (Journal of Computational Mathematics, 2004)
The three-dimensional nonlinear Schrödinger equation with weakly damped that possesses a global attractor is considered. The dynamical properties of the discrete dynamical system which generate by a class of finite difference scheme are analysed. The existence of global attractor is proved for the discrete dynamical system.