Analysis of the damped nonlinear space-fractional Schrodinger equation

In this paper, we verify the unique existence of the global smooth solution of the damped nonlinear space-fractional Schrodinger (DNFS) equation and show it follows a conformal mass conservation law. We propose a conformal mass-preserving linearized scheme. It is rigorously proved that this scheme preserves the discrete conformal mass. Furthermore, we prove that the proposed scheme admits a unique solution and is of second order convergence in space and first order convergence in time. Some numerical experiments are carried out to validate the theoretical analysis. (C) 2017 Elsevier Inc. All rights reserved.