Lie symmetry analysis and exact solutions for the extended mKdV equation
type: Item
instance of: scholarly article
title: Lie symmetry analysis and exact solutions for the extended mKdV equation
zbMATH Open document ID: 1223.37079
author: Han-Ze Liu
author: Jibin Li
published in: Acta Applicandae Mathematicae
publication date: 2010-05-26T00:00:00Z
review text: This paper concerns solutions of an extended mKdV equation of the form \[ u_t +a_1 u_{xxx} + a_2 u_x +a_3 u u_x + a_4 u^2 u_x = 0, \] where \(u = u(x,t)\) is an unknown function and the parameters \(a_i\) are real numbers with \(a_1 a_4 \neq 0\). Its exact solutions are obtained by using the method of Lie symmetry analysis as well as the method of dynamical systems, including the bifurcation and traveling wave solutions. The authors determine the conditions of the existence of such solutions and obtain exact analytic solutions by using the power series method.
reviewed by: Min Ho Lee
Mathematics Subject Classification ID: 37K05
Mathematics Subject Classification ID: 17B80
Mathematics Subject Classification ID: 35A30
Mathematics Subject Classification ID: 35Q53
zbMATH DE Number: 5712207
zbMATH Keywords: Lie symmetry analysis
zbMATH Keywords: bifurcations
zbMATH Keywords: traveling wave solutions
zbMATH Keywords: extended mKdV equations
MaRDI profile type: Publication
full work available at URL: s10440-008-9362-8
OpenAlex ID: W2041676211
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DOI: 10.1007/S10440-008-9362-8
description: scientific article; zbMATH DE number 5712207