Contact symmetry algebras of scalar ordinary differential equations
type: Item
instance of: scholarly article
title: Contact symmetry algebras of scalar ordinary differential equations
zbMATH Open document ID: 1015.34026
DOI: 10.1023/A:1015030931611
author: C. Wafo Soh
author: F. M. Mahomed
author: Changzheng Qu
published in: Nonlinear Dynamics
publication date: 2002-08-20T00:00:00Z
review text: The authors investigate third-order ordinary differential equations with respect to existence of irreducible contact symmetries and show that such an equation admits an irreducible contact symmetry algebra if and only if this equation may be transformed by a contact transformation into the equation \(y'''=0\). Furthermore, the classification of third-order equations by point symmetries is related to the question to interpret the corresponding Lie algebras of point symmetries, resp. of contact symmetries, as subalgebras of the symmetry algebras in the cases of maximal dimension (7 point symmetries, resp. 10 contactsymmetries) and of symmetry breaking. It is also proved that a fourth-order equation can not admit an irreducible contact symmetry algebra, for the order \(n\geq 5\), ODEs with nontrivial contact symmetry algebras are characterized.
Mathematics Subject Classification ID: 34C14
Mathematics Subject Classification ID: 17B66
zbMATH DE Number: 1784468
zbMATH Keywords: existence
zbMATH Keywords: irreducible contact symmetries
zbMATH Keywords: contact transformation
reviewed by: Günter Czichowski
MaRDI profile type: Publication
full work available at URL: a:1015030931611
OpenAlex ID: W173459151
description: scientific article; zbMATH DE number 1784468