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

Jianbo Cui; Jialin Hong; Zhihui Liu; Weien Zhou

doi:10.1016/j.jcp.2017.04.029

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

Jianbo Cui, Jialin Hong, Zhihui Liu, Weien Zhou

Research output: Journal article publication › Journal article › Academic research › peer-review

16 Citations (Scopus)

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.

Original language	English
Pages (from-to)	267-285
Number of pages	19
Journal	Journal of Computational Physics
Volume	342
DOIs	https://doi.org/10.1016/j.jcp.2017.04.029
Publication status	Published - 1 Aug 2017
Externally published	Yes

Keywords

Nonlinear Schrödinger equation
Stochastic symplectic and multi-symplectic schemes
Stochastic symplectic and multi-symplectic structures
White noise dispersion

ASJC Scopus subject areas

Numerical Analysis
Modelling and Simulation
Physics and Astronomy (miscellaneous)
Physics and Astronomy(all)
Computer Science Applications
Computational Mathematics
Applied Mathematics

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10.1016/j.jcp.2017.04.029

Cite this

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title = "Stochastic symplectic and multi-symplectic methods for nonlinear Schr{\"o}dinger equation with white noise dispersion",

abstract = "We indicate that the nonlinear Schr{\"o}dinger 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.",

keywords = "Nonlinear Schr{\"o}dinger equation, Stochastic symplectic and multi-symplectic schemes, Stochastic symplectic and multi-symplectic structures, White noise dispersion",

author = "Jianbo Cui and Jialin Hong and Zhihui Liu and Weien Zhou",

note = "Funding Information: The authors gratefully thank the anonymous referees for valuable comments and suggestions in improving this paper. This work was supported by National Natural Science Foundation of China (No. 91630312, No. 91530118 and No. 11290142). Publisher Copyright: {\textcopyright} 2017 Elsevier Inc.",

year = "2017",

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doi = "10.1016/j.jcp.2017.04.029",

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journal = "Journal of Computational Physics",

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T1 - Stochastic symplectic and multi-symplectic methods for nonlinear Schrödinger equation with white noise dispersion

AU - Cui, Jianbo

AU - Hong, Jialin

AU - Liu, Zhihui

AU - Zhou, Weien

N1 - Funding Information: The authors gratefully thank the anonymous referees for valuable comments and suggestions in improving this paper. This work was supported by National Natural Science Foundation of China (No. 91630312, No. 91530118 and No. 11290142). Publisher Copyright: © 2017 Elsevier Inc.

PY - 2017/8/1

Y1 - 2017/8/1

N2 - 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.

AB - 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.

KW - Nonlinear Schrödinger equation

KW - Stochastic symplectic and multi-symplectic schemes

KW - Stochastic symplectic and multi-symplectic structures

KW - White noise dispersion

UR - http://www.scopus.com/inward/record.url?scp=85018954757&partnerID=8YFLogxK

U2 - 10.1016/j.jcp.2017.04.029

DO - 10.1016/j.jcp.2017.04.029

M3 - Journal article

AN - SCOPUS:85018954757

VL - 342

SP - 267

EP - 285

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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