A Compact Scheme for Coupled Stochastic Nonlinear Schrödinger Equations (Communications in Computational Physics, 2018)
In this paper, we propose a compact scheme to numerically study the coupledstochastic nonlinear Schrödinger equations. We prove that the compact schemepreserves the discrete stochastic multi-symplectic conservation law, discrete chargeconservation law and discrete energy evolution law almost surely. Numerical experimentsconfirm well the theoretical analysis results. Furthermore, we present a detailednumerical investigation of the optical phenomena based on the compact scheme. Bynumerical experiments for various amplitudes of noise, we find that the noise acceleratesthe oscillation of the soliton and leads to the decay of the solution amplitudes withrespect to time. In particular, if the noise is relatively strong, the soliton will be totallydestroyed. Meanwhile, we observe that the phase shift is sensibly modified by thenoise. Moreover, the numerical results present inelastic interaction which is differentfrom the deterministic case.