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Title: Stochastic symplectic and multi-symplectic methods for nonlinear Schrödinger equation with white noise dispersion

Abstract

We indicate that the nonlinear Schrödinger equation with white noise dispersion possesses stochastic symplectic and multi-symplectic structures. Based on these structures, we propose the stochastic symplectic and multi-symplectic methods, which preserve the continuous and discrete charge conservation laws, respectively. Moreover, we show that the proposed methods are convergent with temporal order one in probability. Numerical experiments are presented to verify our theoretical results.

Authors:
 [1];  [1];  [1];  [2]
  1. Institute of Computational Mathematics and Scientific/Engineering Computing, Chinese Academy of Sciences, Beijing, 100190 (China)
  2. College of Science, National University of Defense Technology, Changsha 410073 (China)
Publication Date:
OSTI Identifier:
22622314
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 342; Other Information: Copyright (c) 2017 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CHARGE CONSERVATION; CONSERVATION LAWS; DISPERSIONS; NOISE; NONLINEAR PROBLEMS; PROBABILITY; SCHROEDINGER EQUATION; STOCHASTIC PROCESSES

Citation Formats

Cui, Jianbo, E-mail: jianbocui@lsec.cc.ac.cn, Hong, Jialin, E-mail: hjl@lsec.cc.ac.cn, Liu, Zhihui, E-mail: liuzhihui@lsec.cc.ac.cn, and Zhou, Weien, E-mail: weienzhou@nudt.edu.cn. Stochastic symplectic and multi-symplectic methods for nonlinear Schrödinger equation with white noise dispersion. United States: N. p., 2017. Web. doi:10.1016/J.JCP.2017.04.029.
Cui, Jianbo, E-mail: jianbocui@lsec.cc.ac.cn, Hong, Jialin, E-mail: hjl@lsec.cc.ac.cn, Liu, Zhihui, E-mail: liuzhihui@lsec.cc.ac.cn, & Zhou, Weien, E-mail: weienzhou@nudt.edu.cn. Stochastic symplectic and multi-symplectic methods for nonlinear Schrödinger equation with white noise dispersion. United States. doi:10.1016/J.JCP.2017.04.029.
Cui, Jianbo, E-mail: jianbocui@lsec.cc.ac.cn, Hong, Jialin, E-mail: hjl@lsec.cc.ac.cn, Liu, Zhihui, E-mail: liuzhihui@lsec.cc.ac.cn, and Zhou, Weien, E-mail: weienzhou@nudt.edu.cn. Tue . "Stochastic symplectic and multi-symplectic methods for nonlinear Schrödinger equation with white noise dispersion". United States. doi:10.1016/J.JCP.2017.04.029.
@article{osti_22622314,
title = {Stochastic symplectic and multi-symplectic methods for nonlinear Schrödinger equation with white noise dispersion},
author = {Cui, Jianbo, E-mail: jianbocui@lsec.cc.ac.cn and Hong, Jialin, E-mail: hjl@lsec.cc.ac.cn and Liu, Zhihui, E-mail: liuzhihui@lsec.cc.ac.cn and Zhou, Weien, E-mail: weienzhou@nudt.edu.cn},
abstractNote = {We indicate that the nonlinear Schrödinger equation with white noise dispersion possesses stochastic symplectic and multi-symplectic structures. Based on these structures, we propose the stochastic symplectic and multi-symplectic methods, which preserve the continuous and discrete charge conservation laws, respectively. Moreover, we show that the proposed methods are convergent with temporal order one in probability. Numerical experiments are presented to verify our theoretical results.},
doi = {10.1016/J.JCP.2017.04.029},
journal = {Journal of Computational Physics},
number = ,
volume = 342,
place = {United States},
year = {Tue Aug 01 00:00:00 EDT 2017},
month = {Tue Aug 01 00:00:00 EDT 2017}
}