KMS Of Academy of mathematics and systems sciences, CAS
| Wave-breaking analysis and weak multi-peakon solutions for a generalized cubic-quintic Camassa-Holm type equation | |
| Weng, Weifang1,2; Qiao, Zhijun3; Yan, Zhenya1,2 | |
| 2022-04-05 | |
| Source Publication | MONATSHEFTE FUR MATHEMATIK
 |
| ISSN | 0026-9255 |
| Pages | 47 |
| Abstract | We consider the Cauchy problem and multi-peakon solutions of a generalized cubic-quintic Camassa-Holm (gcqCH) equation, which is actually an extension of the cubic CH equation [alias the Fokas-Olver-Rosenau-Qiao equation in the literature] and the quintic CH equation, and possesses the Hamiltonian structure and conversation law. We first present the blow-up criteria and the precise blow-up quantity in terms of the Moser-type estimate in Sobolev spaces. Then, by using the blow-up quantity and the characteristics associated with the gcqCH equation, we obtain two kinds of sufficient conditions on the initial data to guarantee the occurrence of the wave-breaking phenomenon. Finally, the non-periodic and periodic peakon as well as global N-peakon solutions of the gcqCH equation are also investigated. Particularly, we study the two-peakon dynamical system with the time evolution of their elastic collisions. |
| Keyword | Generalized cubic-quintic CH equation Well-posedness Wave breaking Weak solutions Non-periodic and periodic peakon solutions |
| DOI | 10.1007/s00605-022-01699-w |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | National Natural Science Foundation of China[11925108] ; National Natural Science Foundation of China[11971475] ; UT President's Endowed Professorship[450000123] |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics |
| WOS ID | WOS:000779020200001 |
| Publisher | SPRINGER WIEN |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/60219 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Yan, Zhenya |
| Affiliation | 1.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Math Mechanizat, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Univ Texas Rio Grande Valley, Sch Math & Stat Sci, Edinburg, TX USA |
| Recommended Citation GB/T 7714 | Weng, Weifang,Qiao, Zhijun,Yan, Zhenya. Wave-breaking analysis and weak multi-peakon solutions for a generalized cubic-quintic Camassa-Holm type equation[J]. MONATSHEFTE FUR MATHEMATIK,2022:47. |
| APA | Weng, Weifang,Qiao, Zhijun,&Yan, Zhenya.(2022).Wave-breaking analysis and weak multi-peakon solutions for a generalized cubic-quintic Camassa-Holm type equation.MONATSHEFTE FUR MATHEMATIK,47. |
| MLA | Weng, Weifang,et al."Wave-breaking analysis and weak multi-peakon solutions for a generalized cubic-quintic Camassa-Holm type equation".MONATSHEFTE FUR MATHEMATIK (2022):47. |
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