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

Journal Article · Tue Aug 01 00:00:00 EDT 2017 · Journal of Computational Physics

DOI:https://doi.org/10.1016/J.JCP.2017.04.029· OSTI ID:22622314

Cui, Jianbo ^[1]; Hong, Jialin ^[1]; Liu, Zhihui ^[1]; Zhou, Weien ^[2]

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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)

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.

• OSTI ID: 22622314
• Journal Information: Journal of Computational Physics, Vol. 342; Other Information: Copyright (c) 2017 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CHARGE CONSERVATION
CONSERVATION LAWS
DISPERSIONS
NOISE
NONLINEAR PROBLEMS
PROBABILITY
SCHROEDINGER EQUATION
STOCHASTIC PROCESSES