Dynamical behaviors and new exact bounded travelling wave solutions for the modified Degasperis-Procesi equation
type: Item
instance of: scholarly article
zbMATH Open document ID: 1258.34094
author: Jin-Hua Zhang
author: Bin He
publication date: 2012-09-11T00:00:00Z
full work available at URL: index.html
Mathematics Subject Classification ID: 34C37
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 35Q31
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 35C07
zbMATH DE Number: 6080629
zbMATH Keywords: modified Degasperis-Procesi equation
zbMATH Keywords: dynamical behavior
zbMATH Keywords: special phase orbit
zbMATH Keywords: bounded travelling wave
zbMATH Keywords: exact solution
MaRDI profile type: Publication
title: Dynamical behaviors and new exact bounded travelling wave solutions for the modified Degasperis-Procesi equation
published in: Applied Mathematical Sciences (Ruse)
review text: Consider the partial differential equation NEWLINE\[NEWLINEu_t- u_{xxt}+ 4uu_x= 3u_x u_{xx}+ uu_{xxx}.\tag{\(*\)}NEWLINE\]NEWLINE The authors look for solutions of \((*)\) in the form NEWLINE\[NEWLINEu(x,t)= \mu+ \psi(\xi),\quad \xi= x-ct,NEWLINE\]NEWLINE where \(c>0\) is the wave speed, \(\mu\) is some constant. This problem can be reduced to the study of a planar autonomous system with respect to the existence of heteroclinic, homoclinic and periodic trajectories. The authors establish under special relations between \(c\) and \(\mu\) such solutions.
reviewed by: Klaus R. Schneider
description: scientific article; zbMATH DE number 6080629