Wave-breaking analysis and weak multi-peakon solutions for a generalized cubic-quintic Camassa-Holm type equation

doi:10.1007/s00605-022-01699-w

	Wave-breaking analysis and weak multi-peakon solutions for a generalized cubic-quintic Camassa-Holm type equation
	Weng, Weifang 1,3; Qiao, Zhijun 2; Yan, Zhenya 1,3
刊名	MONATSHEFTE FUR MATHEMATIK
	2022-04-05
页码	47
关键词	Generalized cubic-quintic CH equation Well-posedness Wave breaking Weak solutions Non-periodic and periodic peakon solutions
ISSN号	0026-9255
DOI	10.1007/s00605-022-01699-w
英文摘要	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.
资助项目	National Natural Science Foundation of China[11925108] ; National Natural Science Foundation of China[11971475] ; UT President's Endowed Professorship[450000123]
WOS研究方向	Mathematics
语种	英语
出版者	SPRINGER WIEN
WOS记录号	WOS:000779020200001
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/60218]
专题	中国科学院数学与系统科学研究院
通讯作者	Yan, Zhenya
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Math Mechanizat, Beijing 100190, Peoples R China 2.Univ Texas Rio Grande Valley, Sch Math & Stat Sci, Edinburg, TX USA 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 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.