A Compact Scheme for Coupled Stochastic Nonlinear Schrödinger Equations. (5th December 2016)

• Record Type: Journal Article
• Authors: Chen, Chuchu; Hong, Jialin; Ji, Lihai; Kong, Linghua
• Is Part Of: Communications in computational physics. Volume 21:Number 1(2017:Jan.)
• Page Start: 93
• Page End: 125
• Publication Date: 2016-12-05
• Subjects: 60H15, -- 60H35, -- 37K05; Coupled stochastic nonlinear Schrödinger equations, -- compact scheme, -- stochastic multi-symplectic conservation law, -- energy evolution law, -- charge conservation law, -- soliton evolution, -- soliton interaction; Mathematical physics -- Data processing -- Periodicals; Physics -- Data processing -- Periodicals; 530.150285
• DOI: 10.4208/cicp.300815.180416a
• Languages: English
• ISSNs: 1815-2406

Abstract

Abstract: In this paper, we propose a compact scheme to numerically study the coupled stochastic nonlinear Schrödinger equations. We prove that the compact scheme preserves the discrete stochastic multi-symplectic conservation law, discrete charge conservation law and discrete energy evolution law almost surely. Numerical experiments confirm well the theoretical analysis results. Furthermore, we present a detailed numerical investigation of the optical phenomena based on the compact scheme. By numerical experiments for various amplitudes of noise, we find that the noise accelerates the oscillation of the soliton and leads to the decay of the solution amplitudes with respect to time. In particular, if the noise is relatively strong, the soliton will be totally destroyed. Meanwhile, we observe that the phase shift is sensibly modified by the noise. Moreover, the numerical results present inelastic interaction which is different from the deterministic case.