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

被引：0
作者：
Weifang Weng
Zhijun Qiao
Zhenya Yan
机构：
[1] Academy of Mathematics and Systems Science,Key Laboratory of Mathematics Mechanization
[2] Chinese Academy of Sciences,School of Mathematical Sciences
[3] University of Chinese Academy of Sciences,School of Mathematical and Statistical Sciences
[4] University of Texas Rio Grande Valley,undefined
来源：
Monatshefte für Mathematik | 2023年 / 200卷
关键词：
Generalized cubic–quintic CH equation; Well-posedness; Wave breaking; Weak solutions; Non-periodic and periodic peakon solutions; 35B30; 35G25; 35B44; 35Q35;
D O I：
暂无
中图分类号：
学科分类号：
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.
引用
收藏
页码：667 / 713
页数：46
相关论文
共 106 条
[1]  
Camassa R(1993)An integrable shallow water equation with peaked solitons Phys. Rev. Lett. 71 1661-1664
[2]  
Holm D(1981)Symplectic structures, their Backlund transformation and hereditary symmetries Phys. D 4 47-66
[3]  
Fokas A(1996)Tri-Hamiltonian duality between solitons and solitary-wave solutions having compact support Phys. Rev. E 53 1900-1906
[4]  
Fuchssteiner B(1994)The geometry of peaked solitons and billiard solutions of a class of integrable PDE‘s Lett. Math. Phys. 32 137-151
[5]  
Olver P(1999)Multi-peakons and a theorem of Stieltjes, Multi-peakons and a theorem of Stieltjes Inverse Prob. 15 L1-L4
[6]  
Rosenau P(2000)Multipeakons and the classical moment problem Adv. Math. 154 229-57
[7]  
Alber MS(1999)The Camassa Holm equation: conserved quantities and the initial value problem Phys. Lett. A 259 371-376
[8]  
Camassa R(1998)Acoustic scattering and the extended Korteweg-de Vries hierarchy Adv. Math. 140 190-206
[9]  
Holm DD(1999)A shallow water equation on the circle Commun. Pure Appl. Math. 52 949-982
[10]  
Marsden JE(2006)Inverse scattering transform for the Camassa-Holm equation Inverse Prob. 22 2197-2207
12345678910