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Stochastic Multi-Symplectic Integrator for Stochastic Nonlinear Schrödinger Equation

Published online by Cambridge University Press:  03 June 2015

Shanshan Jiang ,
Lijin Wang  and
Jialin Hong
Shanshan Jiang*
Affiliation:
College of Science, Beijing University of Chemical Technology, Beijing 100029, P.R. China
Lijin Wang*
Affiliation:
School of Mathematical Sciences, Graduate University of Chinese Academy of Sciences, Beijing 100049, P.R. China
Jialin Hong*
Affiliation:
State Key Laboratory of Scientific and Engineering Computing, Institute of ComputationalMathematics and Scientific/Engineering Computing, Academy of Mathematics and System Science, Chinese Academy of Sciences, P.O. Box 2719, Beijing 100190, P.R. China
*
Corresponding author.Email:jiangss@mail.buct.edu.cn
Email:ljwang@gucas.ac.cn
Email:hjl@lsec.cc.ac.cn
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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 Schrödinger 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.

Keywords

60H1565M0665P10Stochastic nonlinear Schrödinger equationsstochastic multi-symplectic Hamiltonian systemsmulti-symplectic integrators
Type
Research Article
Information
Communications in Computational Physics , Volume 14 , Issue 2 , August 2013 , pp. 393 - 411
Copyright
Copyright © Global Science Press Limited 2013

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