• 论文 •

### 带乘性噪声的空间分数阶随机非线性Schrödinger方程的广义多辛算法

1. 国防科技大学数学系, 长沙 410073
• 收稿日期:2019-05-10 出版日期:2019-12-15 发布日期:2019-11-16
• 基金资助:

国家自然科学基金（11571366），湖南省自然科学基金（S2017JJQNJJ0764）和国防科技大学科研计划项目（ZK17-03-27）资助项目.

Liu Ziyuan, Liang Jiarui, Qian Xu, Song Songhe. A GENERALIZED MULTI-SYMPLECTIC METHOD FOR STOCHASTIC SPACE-FRACTIONAL NONLINEAR SCHRÖDINGER EQUATION WITH MULTIPLICATIVE NOISE[J]. Mathematica Numerica Sinica, 2019, 41(4): 440-452.

### A GENERALIZED MULTI-SYMPLECTIC METHOD FOR STOCHASTIC SPACE-FRACTIONAL NONLINEAR SCHRÖDINGER EQUATION WITH MULTIPLICATIVE NOISE

Liu Ziyuan, Liang Jiarui, Qian Xu, Song Songhe

1. Department of mathematics, National University of Defense Technology, Changsha 410073, China
• Received:2019-05-10 Online:2019-12-15 Published:2019-11-16

The stochastic space-fractional nonlinear Schrödinger equation with multiplicative noise is an important equation which describes the evolution of an open nonlocal quantum system. In this paper we prove that this system is an infinite-dimensional stochastic fractional Hamiltonian system, and satisfies both the mass and the generalized multi-symplectic conservation law. After that, with the Fourier pseudo-spectral approximation to the spatial fractional Laplacian operator and the implicit mid-point method for time discretization, we propose a mass-conserving generalized stochastic multi-symplectic method. Numerical simulations are presented for soliton solution and plane wave solution. The results demonstrate the effectiveness and conservative property of the proposed methods. Furthermore, the results show that the mean square convergence order on time is approximately 0.5 to 1.

MR(2010)主题分类:

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