A Compact Scheme for Coupled Stochastic Nonlinear Schrödinger Equations
A Compact Scheme for Coupled Stochastic Nonlinear Schrödinger Equations
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DOI：
10.4208/cicp.300815.180416a
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发表时间：
2017
影响因子：
3.7
通讯作者：
Chuchu Chen;Jialin Hong;Lihai Ji;L. Kong
中科院分区：
文献类型：
--
作者：
Chuchu Chen;Jialin Hong;Lihai Ji;L. Kong
本文提出了一种紧致格式来数值研究耦合随机非线性薛定谔方程。我们证明了紧致格式几乎必然保持离散随机多辛守恒律、离散电荷守恒律和离散能量演化律。数值实验很好地证实了理论分析结果。此外，我们提出了一个详细的数值研究的光学现象的紧凑计划的基础上。通过对不同振幅噪声的数值实验，我们发现噪声加速了孤子的振荡，并导致孤子解的振幅随时间衰减。特别是当噪声较强时，孤子将被完全破坏。同时，我们观察到相移被噪声敏感地修改。此外，数值结果呈现出非弹性相互作用，这是不同于确定性的情况。AMS科目分类：60H15、60H35、37K05
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. AMS subject classifications: 60H15, 60H35, 37K05