修正Camassa Holm-Kadomtsev Petviashvili方程的尖峰解  

Peaked Weak Solutions for the Modified Camassa-Holm-Kadomtsev-Petviashvili Equation

作　　者：李志刚 毛辉 LI ZHIGANG;MAO Hui(Department of Fundamental Courses,Shanci Institute of Technology,Yangquan 045000,China;School of Mathematics and Statistics,Nanning Normal University,Nanning 530001,China)

机构地区：[1]山西工程技术学院基础课教学部,阳泉045000 [2]南宁师范大学数学与统计学院,南宁530001

出　　处：《应用数学学报》2025年第2期251-262,共12页Acta Mathematicae Applicatae Sinica

基　　金：山西省高等学校科技创新项目资助(2021L593);2022年第一批博士毕业生、博士后研究人员来晋工作奖励资金(科研经费)项目(2022PT-04);山西工程技术学院2021年科研启动经费项目(2021QD-20);国家自然科学基金(12261061);广西自然科学基金(2022GXNSFAA035598)资助。

摘　　要：本文研究了一个新的具有双哈密顿结构的修正CH-KP方程.通过对解的形式做适当的拟设,导出了该方程的尖峰孤子解,双尖峰孤子解,以及周期尖峰孤子解,并得到了一种新的不会在1+1维情形下存在的双尖峰孤子解.In this paper,we study a new(2+1)dimensional modified Camassa-Holm equation,which is integrable since it admits bi-Hamiltonian structure.The aim of this paper is to study the existence of peakons for such equation.The suitable definitions of weak solutions both on real line and circle are defined.The single-peakon,two-peakon,and periodic peakon of such equation are derived.A new type of two-peakon is obtained,and the reason why such phenomena may not occur in(1+1)dimension case is also illustrated.

关 键 词：修正CH-KP方程 行波解 尖峰孤子解 周期尖峰解 

分 类 号：O175.24[理学—数学]