Optimal system and group invariant solutions for a nonlinear wave equation.
type: Item
instance of: scholarly article
title: Optimal system and group invariant solutions for a nonlinear wave equation.
zbMATH Open document ID: 1036.35010
DOI: 10.1016/S1007-5704(03)00018-2
author: G. H. Maluleke
author: D. P. Mason
published in: Communications in Nonlinear Science and Numerical Simulation
publication date: 2004-01-06T00:00:00Z
review text: In this paper, the equation \[ \frac{\partial\phi}{\partial t}+\frac{\partial}{\partial z} \Biggl[\phi^n \biggl(1-\frac {\partial} {\partial z} \biggl(\frac{1}{\phi^m} \frac{\partial\phi}{\partial t}\biggr) \biggr) \Biggr]=0 \] is considered. An optimal system for the algebra of point symmetries of the equation is investigated. For \(n=0, m=4/3\), it is shown that the equation can be reduced to the special case of Ermakov-Pinney equation. For \(n=0\), \(m\neq 4/3\), \(m\neq 0\), it is shown that the equation can be reduced either to a first-order or a second-order ordinary differential equation.
Mathematics Subject Classification ID: 35A30
Mathematics Subject Classification ID: 58J70
zbMATH DE Number: 2021953
zbMATH Keywords: point symmetry
zbMATH Keywords: Ermakov-Pinney equation
reviewed by: Valeriy Yumaguzhin
MaRDI profile type: Publication
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full work available at URL: s1007-5704(03)00018-2
OpenAlex ID: W2084622069
description: scientific article; zbMATH DE number 2021953