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Symplectic simulation of dark solitons motion for nonlinear Schrodinger equation
Zhu, Beibei1; Tang, Yifa2,3; Zhang, Ruili4; Zhang, Yihao2,3
2019-08-01
Source PublicationNUMERICAL ALGORITHMS
ISSN1017-1398
Volume81Issue:4Pages:1485-1503
AbstractIn 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.
KeywordNonlinear Schrodinger equation Ablowitz-ladik model Symplectic methods K-symplectic methods Invariants
DOI10.1007/s11075-019-00708-8
Language英语
Funding ProjectNational Natural Science Foundation of China[11771438] ; National Center for Mathematics and Interdisciplinary Sciences, CAS
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000478001200019
PublisherSPRINGER
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/35356
Collection中国科学院数学与系统科学研究院
Corresponding AuthorZhu, Beibei
Affiliation1.Chinese Acad Sci, Natl Ctr Math & Interdisciplinary Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
2.Chinese Acad Sci, LSEC, ICMSEC, Acad Math & Syst Sci, Beijing 100190, Peoples R China
3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
4.Beijing Jiaotong Univ, Sch Sci, Beijing 100044, Peoples R China
Recommended Citation
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.
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