Analysis of the damped nonlinear space-fractional Schrödinger equation

Jiarui Liang, Songhe Song, Weien Zhou and Hao Fu

Applied Mathematics and Computation, 2018, vol. 320, issue C, 495-511

Abstract: In this paper, we verify the unique existence of the global smooth solution of the damped nonlinear space-fractional Schrödinger (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.

Keywords: Damped nonlinear space-fractional Schrödinger equation; Global smooth solution; Conformal mass-preserving linearized scheme; Stability and convergence (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:320:y:2018:i:c:p:495-511

DOI: 10.1016/j.amc.2017.10.010

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