Symplectic simulation of dark solitons motion for nonlinear Schrodinger equation

doi:10.1007/s11075-019-00708-8

	Symplectic simulation of dark solitons motion for nonlinear Schrodinger equation
	Zhu, Beibei 4; Tang, Yifa 2,3; Zhang, Ruili 1; Zhang, Yihao 2,3
刊名	NUMERICAL ALGORITHMS
	2019-08-01
卷号	81 期号:4 页码:1485-1503
关键词	Nonlinear Schrodinger equation Ablowitz-ladik model Symplectic methods K-symplectic methods Invariants
ISSN号	1017-1398
DOI	10.1007/s11075-019-00708-8
英文摘要	In this paper, we study symplectic simulation of dark solitons motion of nonlinear Schrodinger equation (NLSE). The Ablowitz-Ladik model (A-L model) of NLSE can be expressed as a non-canonical Hamiltonian system. By using splitting technique, we construct explicit splitting K-symplectic methods for the A-L model. On the other hand, the A-L model can be transformed into a canonical system and standard symplectic methods can be employed to perform numerical simulation. A second order K-symplectic method and a second order symplectic method are employed to simulate one dark soliton and two dark solitons motion for the A-L model and its canonicalized system respectively. By comparing with a third-order non-symplectic Runge-Kutta method, we show the superiorities of the two symplectic methods in long-term tracking the motion of dark solitons and preserving the invariants. We also compare the CPU times of K-symplectic methods and standard symplectic methods and show that the former ones are more efficient. The energy-preserving scheme is also applied for non-canonical Hamiltonian systems. The numerical results demonstrate that the K-symplectic methods can nearly preserve the energy, the discrete invariants of A-L model and conserved quantities of NLSE, but the energy-preserving scheme can only exactly preserve the energy.
资助项目	National Natural Science Foundation of China[11771438] ; National Center for Mathematics and Interdisciplinary Sciences, CAS
WOS研究方向	Mathematics
语种	英语
出版者	SPRINGER
WOS记录号	WOS:000478001200019
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/35355]
专题	中国科学院数学与系统科学研究院
通讯作者	Zhu, Beibei
作者单位	1.Beijing Jiaotong Univ, Sch Sci, Beijing 100044, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Chinese Acad Sci, LSEC, ICMSEC, Acad Math & Syst Sci, Beijing 100190, Peoples R China 4.Chinese Acad Sci, Natl Ctr Math & Interdisciplinary Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Zhu, Beibei,Tang, Yifa,Zhang, Ruili,et al. Symplectic simulation of dark solitons motion for nonlinear Schrodinger equation[J]. NUMERICAL ALGORITHMS,2019,81(4):1485-1503.
APA	Zhu, Beibei,Tang, Yifa,Zhang, Ruili,&Zhang, Yihao.(2019).Symplectic simulation of dark solitons motion for nonlinear Schrodinger equation.NUMERICAL ALGORITHMS,81(4),1485-1503.
MLA	Zhu, Beibei,et al."Symplectic simulation of dark solitons motion for nonlinear Schrodinger equation".NUMERICAL ALGORITHMS 81.4(2019):1485-1503.