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A Numerical Study of the 3-Periodic Wave Solutions to Toda-Type Equations
Thang, Yingnan1; Hu, Xingbiao2,3; He, Yi4; Sun, Jianqing5
2019-08-01
Source PublicationCOMMUNICATIONS IN COMPUTATIONAL PHYSICS
ISSN1815-2406
Volume26Issue:2Pages:579-598
AbstractIn this paper, we present an efficient numerical scheme to calculate N-periodic wave solutions to the Toda-type equations. The starting point is the algebraic condition for having N-periodic wave solutions proposed by Akira Nakamura. The basic idea is to formulate the condition as a nonlinear least square problem and then use the Gauss-Newton method to solve it. By use of this numerical scheme, we calculate the 3-periodic wave solutions to some discrete integrable equations such as the Toda lattice equation, the Lotka-Volterra equation, the differential-difference KP equation and so on.
KeywordToda-type equation N-periodicwave solution Riemann's theta-function Gauss-Newton method
Funding OrganizationNational Natural Science Foundation of China ; National Natural Science Foundation of China ; Natural Science Foundation of Jiangsu Province Colleges and Universities ; Natural Science Foundation of Jiangsu Province Colleges and Universities ; Jiangsu Planned Projects for Postdoctoral Research Funds ; Jiangsu Planned Projects for Postdoctoral Research Funds ; Fundamental Research Funds for the Central Universities ; Fundamental Research Funds for the Central Universities ; Youth Innovation Promotion Association CAS - Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD) ; Youth Innovation Promotion Association CAS - Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD) ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; Natural Science Foundation of Jiangsu Province Colleges and Universities ; Natural Science Foundation of Jiangsu Province Colleges and Universities ; Jiangsu Planned Projects for Postdoctoral Research Funds ; Jiangsu Planned Projects for Postdoctoral Research Funds ; Fundamental Research Funds for the Central Universities ; Fundamental Research Funds for the Central Universities ; Youth Innovation Promotion Association CAS - Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD) ; Youth Innovation Promotion Association CAS - Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD) ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; Natural Science Foundation of Jiangsu Province Colleges and Universities ; Natural Science Foundation of Jiangsu Province Colleges and Universities ; Jiangsu Planned Projects for Postdoctoral Research Funds ; Jiangsu Planned Projects for Postdoctoral Research Funds ; Fundamental Research Funds for the Central Universities ; Fundamental Research Funds for the Central Universities ; Youth Innovation Promotion Association CAS - Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD) ; Youth Innovation Promotion Association CAS - Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD) ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; Natural Science Foundation of Jiangsu Province Colleges and Universities ; Natural Science Foundation of Jiangsu Province Colleges and Universities ; Jiangsu Planned Projects for Postdoctoral Research Funds ; Jiangsu Planned Projects for Postdoctoral Research Funds ; Fundamental Research Funds for the Central Universities ; Fundamental Research Funds for the Central Universities ; Youth Innovation Promotion Association CAS - Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD) ; Youth Innovation Promotion Association CAS - Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD)
DOI10.4208/cicp.OA-2018-0157
WOS KeywordQUASI-PERIODIC SOLUTIONS ; ALGEBRO-GEOMETRIC CONSTRUCTIONS ; NONLINEAR EVOLUTION-EQUATIONS ; HYPERELLIPTIC THETA-FUNCTIONS ; KDV
Language英语
Funding ProjectNational Natural Science Foundation of China[11401546] ; National Natural Science Foundation of China[11601237] ; National Natural Science Foundation of China[11571358] ; National Natural Science Foundation of China[11871336] ; Natural Science Foundation of Jiangsu Province Colleges and Universities[16KJB110014] ; Jiangsu Planned Projects for Postdoctoral Research Funds[1601054A] ; Fundamental Research Funds for the Central Universities[201562012] ; Youth Innovation Promotion Association CAS - Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD)
Funding OrganizationNational Natural Science Foundation of China ; National Natural Science Foundation of China ; Natural Science Foundation of Jiangsu Province Colleges and Universities ; Natural Science Foundation of Jiangsu Province Colleges and Universities ; Jiangsu Planned Projects for Postdoctoral Research Funds ; Jiangsu Planned Projects for Postdoctoral Research Funds ; Fundamental Research Funds for the Central Universities ; Fundamental Research Funds for the Central Universities ; Youth Innovation Promotion Association CAS - Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD) ; Youth Innovation Promotion Association CAS - Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD) ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; Natural Science Foundation of Jiangsu Province Colleges and Universities ; Natural Science Foundation of Jiangsu Province Colleges and Universities ; Jiangsu Planned Projects for Postdoctoral Research Funds ; Jiangsu Planned Projects for Postdoctoral Research Funds ; Fundamental Research Funds for the Central Universities ; Fundamental Research Funds for the Central Universities ; Youth Innovation Promotion Association CAS - Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD) ; Youth Innovation Promotion Association CAS - Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD) ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; Natural Science Foundation of Jiangsu Province Colleges and Universities ; Natural Science Foundation of Jiangsu Province Colleges and Universities ; Jiangsu Planned Projects for Postdoctoral Research Funds ; Jiangsu Planned Projects for Postdoctoral Research Funds ; Fundamental Research Funds for the Central Universities ; Fundamental Research Funds for the Central Universities ; Youth Innovation Promotion Association CAS - Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD) ; Youth Innovation Promotion Association CAS - Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD) ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; Natural Science Foundation of Jiangsu Province Colleges and Universities ; Natural Science Foundation of Jiangsu Province Colleges and Universities ; Jiangsu Planned Projects for Postdoctoral Research Funds ; Jiangsu Planned Projects for Postdoctoral Research Funds ; Fundamental Research Funds for the Central Universities ; Fundamental Research Funds for the Central Universities ; Youth Innovation Promotion Association CAS - Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD) ; Youth Innovation Promotion Association CAS - Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD)
WOS Research AreaPhysics
WOS SubjectPhysics, Mathematical
WOS IDWOS:000463352200010
PublisherGLOBAL SCIENCE PRESS
Citation statistics
Document Type期刊论文
Identifierhttp://ir.wipm.ac.cn/handle/112942/14009
Collection中国科学院武汉物理与数学研究所
Corresponding AuthorSun, Jianqing
Affiliation1.Nanjing Normal Univ, Sch Math Sci, Nanjing, Jiangsu, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, LSEC, Beijing, Peoples R China
3.Univ Chinese Acad Sci, Sch Math Sci, Beijing, Peoples R China
4.Chinese Acad Sci, Wuhan Inst Phys & Math, Wuhan, Hubei, Peoples R China
5.Ocean Univ China, Sch Math Sci, Qingdao, Shandong, Peoples R China
Recommended Citation
GB/T 7714
Thang, Yingnan,Hu, Xingbiao,He, Yi,et al. A Numerical Study of the 3-Periodic Wave Solutions to Toda-Type Equations[J]. COMMUNICATIONS IN COMPUTATIONAL PHYSICS,2019,26(2):579-598.
APA Thang, Yingnan,Hu, Xingbiao,He, Yi,&Sun, Jianqing.(2019).A Numerical Study of the 3-Periodic Wave Solutions to Toda-Type Equations.COMMUNICATIONS IN COMPUTATIONAL PHYSICS,26(2),579-598.
MLA Thang, Yingnan,et al."A Numerical Study of the 3-Periodic Wave Solutions to Toda-Type Equations".COMMUNICATIONS IN COMPUTATIONAL PHYSICS 26.2(2019):579-598.
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