Finite-dimensional global attractor for a semi-discrete fractional nonlinear Schrodinger equation

摘要

We consider a semi-discrete in time Crank-Nicolson scheme to discretize a weakly damped forced nonlinear fractional Schrodinger equation u(t)-i(-)u+i|u|(2)u+u=f for (,1) considered in the the whole space R. We prove that such semi-discrete equation provides a discrete infinite-dimensional dynamical system in H(R) that possesses a global attractor in H(R). We show also that if the external force is in a suitable weighted Lebesgue space, then this global attractor has a finite fractal dimension. Copyright (c) 2017 John Wiley & Sons, Ltd.