The dynamics of conservative peakons in a family of U(1)-invariant integrable equations of NLS-Hirota type
文献类型：期刊论文
| 作者 | Anco, Stephen C.1; Chang, Xiangke2,3,4 ; Szmigielski, Jacek4
|
| 刊名 | STUDIES IN APPLIED MATHEMATICS
 |
| 出版日期 | 2018-11-01 |
| 卷号 | 141期号:4页码:680-713 |
| 关键词 | inverse problems Pade approximations peakons tri-Hamiltonian weak solutions |
| ISSN号 | 0022-2526 |
| DOI | 10.1111/sapm.12241 |
| 英文摘要 | 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. |
| 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 |
| 语种 | 英语 |
| WOS记录号 | WOS:000449563000008 |
| 出版者 | WILEY |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/31715]  |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
浏览0
下载0
收藏0
其他版本
除非特别说明，本系统中所有内容都受版权保护，并保留所有权利。