几个多分量Camassa-Holm类型方程的尖峰孤子解和扭结型解

发布时间：2018-06-20 22:41

本文选题：多分量CH类型方程 + 尖峰孤子解　；参考：《内蒙古师范大学》2017年硕士论文

【摘要】：Camassa-Holm(CH)方程有许多独特的数学性质和广泛的物理意义.CH方程的解及其性质的研究极大地丰富了潜水波理论和孤立子理论,这吸引着专家学者的广泛关注.最近,人们将CH方程拓展到耦合多分量的情形,并进行大批的研究.求解方程的尖峰孤子解与扭结型解并分析其动态行为是非线性方程理论的一个重要方面,本文将主要研究耦合多分量的CH类型方程的多重尖峰孤解子与扭结型解.第一章介绍了浅水波理论的研究背景、研究现状及其意义.第二章得到了几个多分量CH类型方程的尖峰孤子解,重点研究了二重尖峰孤子解并通过图形对其动态行为进行了简单分析.第三章研究了可积意义下耦合的二分量CH类型方程,并在不同的参数条件下,得到了多重扭结型解.最后,对全文进行了总结,并做了进一步展望.
[Abstract]:Camassa-Holmschach equation has many unique mathematical properties and extensive physical meaning. The research on the solution and properties of the Ch equation has greatly enriched the theory of submersible wave and soliton theory, which has attracted extensive attention of experts and scholars. Recently, the Ch equation has been extended to the coupled multicomponent case, and a large number of studies have been carried out. In this paper, we will study the multi-spike soliton solution and the kink type solution of the coupled multi-component Ch type equation, and analyze their dynamic behavior in an important aspect of the theory of nonlinear equations. The first chapter introduces the research background, research status and significance of shallow water wave theory. In the second chapter, we obtain the peak soliton solutions of several multicomponent Ch type equations, and focus on the double spike soliton solutions. In chapter 3, the coupled two-component Ch type equations in integrable sense are studied, and the multi-kink type solutions are obtained under different parameter conditions. Finally, the full text is summarized, and further prospects are made.
【学位授予单位】：内蒙古师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175.29

【参考文献】