耗散型耦合随机非线性薛定谔方程的性质研究

Properties of coupled damped stochastic nonlinear Schr dinger equation

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得到了广泛的应用.关于随机偏微分方程性质的研究是国内外专家学者关注的热点之一.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,在等离子物理和耗散量子场论中具有重要作用.提出了该方程具有随机共形多辛几何结构,给出了耗散型耦合随机非线性薛定谔方程的随机共形多辛守恒律,以及电荷的平均演化规律和能量演化规律.

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.The research on the properties of stochastic partial differential equations is one of the hot spots in the world.Coupled damped stochastic nonlinear Schr dinger equation,as a special stochastic partial differential equation which plays an important role in plasma physics and dissipative quantum field theory.In this paper,we propose that the equation has a stochastic conformal multi-symplectic geometry and we propose the stochastic conformal multi-symplectic conservation law,the charge average evolution law and the energy evolution law of coupled damped stochastic nonlinear Schr dinger equation.