WELL-POSEDNESS AND PEAKON SOLUTIONS FOR A HIGHER ORDER CAMASSA-HOLM TYPE EQUATION  

高阶Camassa-Holm类方程的适定性和Peakon解

作　　者：CHEN shuang 陈爽(宁波大学数学与统计学院,浙江宁波315211)

机构地区：[1]School of Mathematics and Statistics,Ningbo University,Ningbo 315211,China

出　　处：《数学杂志》2025年第1期57-71,共15页Journal of Mathematics

摘　　要：In this paper,we delve into a generalized higher order Camassa-Holm type equation,(or,an ghmCH equation for short).We establish local well-posedness for this equation under the condition that the initial data uo belongs to the Sobolev space H'(R)for some s>2.In addition,we obtain the weak formulation of this equation and prove the existence of both single peakon solution and a multi-peakon dynamic system.本文研究了广义的高阶Camassa-Holm类方程,简记为ghmCH方程.在s>7/2,初值u0属于Hs(R)的条件下,我们建立了该方程的局部适定性.除此之外,我们获得了该方程的弱形式,并证明了单峰解和多峰动力系统的存在性.

关 键 词：Generalized higher order Camassa-Holm type equation Local well-posedness PEAKON 

分 类 号：O175.2[理学—数学]