Multi-symplectic Runge-Kutta-Nystrom methods for nonlinear Schrodinger equations with variable coefficients

doi:10.1016/j.jcp.2007.06.023

	Multi-symplectic Runge-Kutta-Nystrom methods for nonlinear Schrodinger equations with variable coefficients
	Hong, Jialin; Liu, Xiao-yan ; Li, Chun
	2007-10-01
发表期刊	JOURNAL OF COMPUTATIONAL PHYSICS
ISSN	0021-9991
卷号	226 期号:2 页码:1968-1984
摘要	In this paper, we consider Runge-Kutta-Nystrom (RKN) methods applied to nonlinear Schrodinger equations with variable coefficients (NLSEvc). Concatenating symplectic Nystrom methods in spatial direction and symplectic Runge-Kutta methods in temporal direction for NLSEvc leads to multi-symplectic integrators, i.e. to numerical methods which preserve the multi-symplectic conservation law (MSCL), we present the corresponding discrete version of MSCL. It is shown that the multi-symplectic RKN methods preserve not only the global symplectic structure in time, but also local and global discrete charge conservation laws under periodic boundary conditions. We present a (4-order) multi-symplectic RKN method and use it in numerical simulation of quasi-periodically solitary waves for NLSEvc, and we compare the multi-symplectic RKN method with a non-multi-symplectic RKN method on the errors of numerical solutions, the numerical errors of discrete energy, discrete momentum and discrete charge. The precise conservation of discrete charge under the multi-symplectic RKN discretizations is attested numerically. Some numerical superiorities of the multi-symplectic RKN methods are revealed. (c) 2007 Elsevier Inc. All rights reserved.
关键词	Nonlinear Schrodinger equations multi-symplectic conservation law Runge-Kutta-Nystrom methods charge conservation law
DOI	10.1016/j.jcp.2007.06.023
语种	英语
WOS研究方向	Computer Science ; Physics
WOS类目	Computer Science, Interdisciplinary Applications ; Physics, Mathematical
WOS记录号	WOS:000250209700039
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/4116
专题	计算数学与科学工程计算研究所
通讯作者	Hong, Jialin
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Computing, State Key Lab Sci & Engn Computing, Beijing 100080, Peoples R China 2.NE Normal Univ, Dept Math, Changchun 130024, Peoples R China 3.Chinese Acad Sci, Grad Sch, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Hong, Jialin,Liu, Xiao-yan,Li, Chun. Multi-symplectic Runge-Kutta-Nystrom methods for nonlinear Schrodinger equations with variable coefficients[J]. JOURNAL OF COMPUTATIONAL PHYSICS,2007,226(2):1968-1984.
APA	Hong, Jialin,Liu, Xiao-yan,&Li, Chun.(2007).Multi-symplectic Runge-Kutta-Nystrom methods for nonlinear Schrodinger equations with variable coefficients.JOURNAL OF COMPUTATIONAL PHYSICS,226(2),1968-1984.
MLA	Hong, Jialin,et al."Multi-symplectic Runge-Kutta-Nystrom methods for nonlinear Schrodinger equations with variable coefficients".JOURNAL OF COMPUTATIONAL PHYSICS 226.2(2007):1968-1984.