The dynamics of conservative peakons in a family of U(1)-invariant integrable equations of NLS-Hirota type

doi:10.1111/sapm.12241

	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, Jacek 4
	2018-11-01
发表期刊	STUDIES IN APPLIED MATHEMATICS
ISSN	0022-2526
卷号	141 期号:4 页码:680-713
摘要	The 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.
关键词	inverse problems Pade approximations peakons tri-Hamiltonian weak solutions
DOI	10.1111/sapm.12241
语种	英语
资助项目	National 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研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000449563000008
出版者	WILEY
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/31716
专题	计算数学与科学工程计算研究所
通讯作者	Szmigielski, Jacek
作者单位	1.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
推荐引用方式 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.