Analysis of the damped nonlinear space-fractional Schrodinger equation

作者：Liang, Jiarui^*; Song, Songhe; Zhou, Weien; Fu, Hao

来源：Applied Mathematics and Computation, 2018, 320: 495-511.

DOI：10.1016/j.amc.2017.10.010

• Damped nonlinear space-fractional
• Schrodinger equation
• Global smooth solution
• Conformal mass-preserving linearized scheme
• Stability and convergence

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.

• 出版日期2018-3-1
• 单位中国人民解放军国防科学技术大学