New explicit periodic wave solutions and their limits for modified form of Camassa-Holm equation
type: Item
instance of: scholarly article
title: New explicit periodic wave solutions and their limits for modified form of Camassa-Holm equation
zbMATH Open document ID: 1223.34070
author: Quan-Di Wang
author: Min-Ying Tang
published in: Acta Mathematicae Applicatae Sinica. English Series
publication date: 2010-09-20T00:00:00Z
review text: This paper is devoted to the study of the following nonlinear equation \[ u_t+2ku_x-u_{xxt}+au^2u_x=2u_xu_{xx}+uu_{xxx}, \] which is a modified form of the Camassa-Holm equation. Using the bifurcation method of dynamical systems, some new explicit periodic wave solutions in terms of Jacobian elliptic functions are constructed. The authors also obtain some explicit solitary wave solutions in terms of hyperbolic functions via the limits of the explicit periodic wave solutions.
Mathematics Subject Classification ID: 34C37
Mathematics Subject Classification ID: 34A05
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 35C07
zbMATH DE Number: 5788812
zbMATH Keywords: Camassa-Holm equation
zbMATH Keywords: periodic solution
zbMATH Keywords: bifurcation method
zbMATH Keywords: solitary wave solutions
MaRDI profile type: Publication
full work available at URL: s10255-008-8013-1
OpenAlex ID: W2065775750
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DOI: 10.1007/S10255-008-8013-1
description: scientific article; zbMATH DE number 5788812