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Volume 14, Issue 2
Stochastic Multi-Symplectic Integrator for Stochastic Nonlinear Schrödinger Equation

Shanshan Jiang, Lijin Wang & Jialin Hong

DOI: 10.4208/cicp.230212.240812a

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

Published online: 2014-08

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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.


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@Article{CiCP-14-393, author = {Shanshan Jiang, Lijin Wang and Jialin Hong}, title = {Stochastic Multi-Symplectic Integrator for Stochastic Nonlinear Schrödinger Equation}, journal = {Communications in Computational Physics}, year = {2014}, volume = {14}, number = {2}, pages = {393--411}, 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.


}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.230212.240812a}, url = {http://global-sci.org/intro/article_detail/cicp/7165.html} }
TY - JOUR T1 - Stochastic Multi-Symplectic Integrator for Stochastic Nonlinear Schrödinger Equation AU - Shanshan Jiang, Lijin Wang & Jialin Hong JO - Communications in Computational Physics VL - 2 SP - 393 EP - 411 PY - 2014 DA - 2014/08 SN - 14 DO - http://doi.org/10.4208/cicp.230212.240812a UR - https://global-sci.org/intro/article_detail/cicp/7165.html KW - AB -

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.


Shanshan Jiang, Lijin Wang and Jialin Hong. (2014). Stochastic Multi-Symplectic Integrator for Stochastic Nonlinear Schrödinger Equation. Communications in Computational Physics. 14 (2). 393-411. doi:10.4208/cicp.230212.240812a
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