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The dynamics of conservative peakons in a family of U(1)-invariant integrable equations of NLS-Hirota type
Anco, Stephen C.1; Chang, Xiangke2,3,4; Szmigielski, Jacek4
2018-11-01
Source PublicationSTUDIES IN APPLIED MATHEMATICS
ISSN0022-2526
Volume141Issue:4Pages:680-713
AbstractThe tri-Hamiltonian splitting method applied to the Hirota hierarchy has yielded two U(1)-invariant nonlinear Partial Differential Equations (PDEs) that admit peakons (nonsmooth solitons). In the present paper, these two peakon PDEs are generalized to a family of U(1)-invariant peakon PDEs parameterized by the real projective line RP1. All equations in this family are shown to possess conservative peakon solutions (whose Sobolev H-1(R) norm is time invariant). The Hamiltonian structure for the sector of conservative peakons is identified and the peakon Ordinary Differential Equations (ODEs) are shown to be Hamiltonian with respect to several Poisson structures. As the main result, it is shown that inverse spectral methods allow one to solve explicitly the dynamics of conservative peakons using explicit solutions to a certain interpolation problem. The graphs of multipeakon solutions confirm the existence of multipeakon breathers as well as asymptotic formation of pairs of two peakon bound states in the nonperiodic time domain.
Keywordinverse problems Pade approximations peakons tri-Hamiltonian weak solutions
DOI10.1111/sapm.12241
Language英语
Funding ProjectNational Natural Science Foundation of China[11701550] ; National Natural Science Foundation of China[11731014] ; Natural Sciences andEngineering Research Council of Canada ; Pacific Institute for Mathematical Sciences ; Department of Mathematics and Statistics, University of Saskatchewan
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000449563000008
PublisherWILEY
Citation statistics
Cited Times:1[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/31716
Collection计算数学与科学工程计算研究所
Affiliation1.Brock Univ, Dept Math & Stat, St Catharines, ON, Canada
2.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing, Peoples R China
3.Univ Chinese Acad Sci, Sch Math Sci, Beijing, Peoples R China
4.Univ Saskatchewan, Dept Math & Stat, 106 Wiggins Rd, Saskatoon, SK S7N 5E6, Canada
Recommended Citation
GB/T 7714
Anco, Stephen C.,Chang, Xiangke,Szmigielski, Jacek. The dynamics of conservative peakons in a family of U(1)-invariant integrable equations of NLS-Hirota type[J]. STUDIES IN APPLIED MATHEMATICS,2018,141(4):680-713.
APA Anco, Stephen C.,Chang, Xiangke,&Szmigielski, Jacek.(2018).The dynamics of conservative peakons in a family of U(1)-invariant integrable equations of NLS-Hirota type.STUDIES IN APPLIED MATHEMATICS,141(4),680-713.
MLA Anco, Stephen C.,et al."The dynamics of conservative peakons in a family of U(1)-invariant integrable equations of NLS-Hirota type".STUDIES IN APPLIED MATHEMATICS 141.4(2018):680-713.
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