We consider a semi-discrete in time Crank-Nicolson scheme to discretize a damped forced nonlinear Schrödinger equation in $2D$. This provides us with a discrete infinite-dimensional dynamical system. We prove the existence of a finite-dimensional global attractor for this dynamical system.
"Semi-discrete weakly damped nonlinear 2-D Schrödinger equation." Differential Integral Equations 23 (3/4) 237 - 252, March/April 2010.