可积的两分量Camassa—Holm方程组的尖峰孤子解及爆破现象  

Peakons and Blow-up Phenomena for an Integrable Two-component Camassa-Holm System

作　　者：张颖[1] 彭聪明[1] Ying ZHANG;Cong Ming PEN(G School of Mathematics and Statistics,Tianshui Normal University,Tianshui 741001,P.R.China)

机构地区：[1]天水师范学院数学与统计学院,天水741001

出　　处：《数学学报（中文版）》2021年第6期895-908,共14页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(11561059);天水师范学院“青蓝”人才工程基金资助项目。

摘　　要：本文讨论了一个可积的两分量Camassa-Holm方程组的周期柯西问题,该模型可看作是修正Camassa-Holm方程的两分量推广.首先给出了显式的周期尖峰孤子解.其次,建立了强解的爆破准则以及强解爆破时初值满足的几个条件.In this paper,we consider the periodic Cauchy problem of an integrable two-component Camassa-Holm system,which can be regarded as a two-component extension of the modified Camassa-Holm equation.First,the periodic peakons are obtained in explicit formulas.Then the precise blow-up scenarios of strong solutions and several conditions on the initial data that produce blow-up of the induced solutions are described in detail.

关 键 词：两分量Camassa-Holm方程组 周期尖峰孤子解 爆破 

分 类 号：O175.2[理学—数学]