Commun. Comput. Phys., 14 (2013), pp. 393-411.


Stochastic Multi-Symplectic Integrator for Stochastic Nonlinear Schrodinger Equation

Shanshan Jiang 1*, Lijin Wang 2, Jialin Hong 3

1 College of Science, Beijing University of Chemical Technology, Beijing 100029, P.R. China.
2 School of Mathematical Sciences, Graduate University of Chinese Academy of Sciences, Beijing 100049, P.R. China.
3 State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and System Science, Chinese Academy of Sciences, P.O. Box 2719, Beijing 100190, P.R. China.

Received 23 February 2012; Accepted (in revised version) 24 August 2012
Available online 12 December 2012
doi:10.4208/cicp.230212.240812a

Abstract

In this paper we propose stochastic multi-symplectic conservation law for stochastic Hamiltonian partial differential equations, and develop a stochastic multi-symplectic method for numerically solving a kind of stochastic nonlinear Schrodinger equations. It is shown that the stochastic multi-symplectic method preserves the multi-symplectic structure, the discrete charge conservation law, and deduces the recurrence relation of the discrete energy. Numerical experiments are performed to verify the good behaviors of the stochastic multi-symplectic method in cases of both solitary wave and collision.

AMS subject classifications: 60H15, 65M06, 65P10

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Key words: Stochastic nonlinear Schrodinger equations, stochastic multi-symplectic Hamiltonian systems, multi-symplectic integrators.

*Corresponding author.
Email: jiangss@mail.buct.edu.cn (S. Jiang), ljwang@gucas.ac.cn (L. Wang), hjl@lsec.cc.ac.cn (J. Hong)
 

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