耗散型随机非线性薛定谔方程的随机共形多辛方法

Stochastic conformal multi-symplectic scheme of damped stochastic nonlinear Schr?dinger equation

随着科学技术的发展及各学科之间的交叉融合,随机偏微分方程逐渐成为研究随机问题的重要数学工具.耗散型随机非线性薛定谔方程作为一类特殊的随机偏微分方程,具有随机共形多辛守恒律.基于数值方法应尽可能地保持原系统的固有性质,在Euler box格式的基础上构造了时空全离散的随机共形Euler box格式,证明了所提出来的随机共形多辛方法能够保持耗散型随机非线性薛定谔方程的离散的随机共形多辛守恒律.

With the development of science and technology and the cross fusion of various disciplines,stochastic partial differential equation has gradually become an important mathematical tool to study stochastic problems.Damped stochastic nonlinear Schr9 dinger equation,as a special stochastic partial differential equation,satisfies stochastic conformal multi-symplectic conservation law.In order to preserve the inherent properties of the original system as much as possible,a stochastic conformal Euler Box scheme is proposed in this paper.It is shown that the stochastic conformal multi-symplectic method preserves the discrete stochastic conformal multi-symplectic conservation law of damped stochastic nonlinear Schr9 dinger equation.