Volume 21, Issue 1
A Compact Scheme for Coupled Stochastic Nonlinear Schrödinger Equations

Chuchu Chen, Jialin Hong, Lihai Ji & Linghua Kong

Commun. Comput. Phys., 21 (2017), pp. 93-125.

Published online: 2018-04

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  • 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.

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@Article{CiCP-21-93, author = {}, title = {A Compact Scheme for Coupled Stochastic Nonlinear Schrödinger Equations}, journal = {Communications in Computational Physics}, year = {2018}, volume = {21}, number = {1}, pages = {93--125}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.300815.180416a}, url = {http://global-sci.org/intro/article_detail/cicp/11233.html} }
TY - JOUR T1 - A Compact Scheme for Coupled Stochastic Nonlinear Schrödinger Equations JO - Communications in Computational Physics VL - 1 SP - 93 EP - 125 PY - 2018 DA - 2018/04 SN - 21 DO - http://doi.org/10.4208/cicp.300815.180416a UR - https://global-sci.org/intro/article_detail/cicp/11233.html KW - AB -

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.

Chuchu Chen, Jialin Hong, Lihai Ji & Linghua Kong. (2020). A Compact Scheme for Coupled Stochastic Nonlinear Schrödinger Equations. Communications in Computational Physics. 21 (1). 93-125. doi:10.4208/cicp.300815.180416a
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