耗散型耦合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 coupled damped stochastic nonlinear Schr dinger equation

作　　者：苗利军 黄驿为 MIAO Lijun;HUANG Yiwei(School of Mathematics,Liaoning Normal University,Dalian 116081,China)

机构地区：[1]辽宁师范大学数学学院,辽宁大连116081

出　　处：《辽宁师范大学学报（自然科学版）》2023年第4期446-450,共5页Journal of Liaoning Normal University:Natural Science Edition

基　　金：国家自然科学基金资助青年项目(12001256);辽宁省教育厅高校基本科研项目(JYTMS20231046)。

摘　　要：随机偏微分方程作为描述受随机环境影响的复杂系统的数学模型,在力学、化学、生物学及经济金融学等领域中都有广泛的应用.耗散型耦合随机非线性薛定谔方程是一类特殊的随机偏微分方程,具有随机共形多辛几何结构,在非线性光学和耗散量子场论中具有重要作用.基于数值格式应尽可能多地保持原随机系统的本质特性,构造了耗散型耦合随机非线性薛定谔方程的随机共形Euler box格式,证明了所提出的随机共形多辛方法能够保持该方程离散的随机共形多辛守恒律.Stochastic partial differential equation,as a mathematical model to describe the complex system affected by stochastic environment,has been widely used in the fields of mechanics,chemistry,biology,economy and finance. Coupled damped stochastic nonlinear Schr dinger equation,as a special stochastic partial differential equation which satisfies the stochastic conformal multi-symplectic geometry and plays an important role in nonlinear optics and dissipative quantum field theory. In order to preserve the inherent properties of the original stochastic system as much as possible,the stochastic conformal Euler box scheme is proposed in this paper,and it is proved that the stochastic conformal multi-symplectic method preserves the discrete stochastic conformal multi-symplectic conservation law of coupled damped stochastic nonlinear Schr dinger equation.

关 键 词：耗散型耦合随机非线性薛定谔方程 随机共形多辛方法 Euler box格式 

分 类 号：O211.9[理学—概率论与数理统计]