Conditional symmetry and new representations of the Galilean algebra for nonlinear parabolic equations
type: Item
instance of: scholarly article
title: Conditional symmetry and new representations of the Galilean algebra for nonlinear parabolic equations
zbMATH Open document ID: 0841.35046
DOI: 10.1007/BF01571094
author: V. I. Chopik
author: W. I. Fushchich
published in: Ukrainian Mathematical Journal
publication date: 1995-03-09T00:00:00Z
review text: The method of conditional symmetry for partial differential equations obtains group invariant solutions of sets of differential equations which do not admit the group as a Lie symmetry group. This is often expressed by demanding that a system extended by additional conditions admits the symmetry. Evenso the operators of conditional symmetry do not generally form an algebra until supplemented by the Lie symmetries of the system. In the current paper, the authors give a constructive method for finding an algebra of conditional invariance for equations of the form \((\partial_t u_a \partial_a) h(x_1,\dots, x_n; u)- \Delta u= F(u)\) under the requirement that the conditional and Lie symmetries together form a basis for the Galilean algebra. They do this by identifying those equations whose Lie symmetries can be extende to the Galilean algebra, constructing a representation for which the equation is an invariant and then finding the supplementary conditions under which the Galilean algebra becomes the algebra of both conditional and Lie symmetries.
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 58J70
zbMATH DE Number: 726950
zbMATH Keywords: conditional symmetry
zbMATH Keywords: algebra of conditional invariance
zbMATH Keywords: Lie symmetries
zbMATH Keywords: Galilean algebra
reviewed by: Christopher Athorne
MaRDI profile type: Publication
cites work: Q3998496
cites work: Q3811042
cites work: Q4023294
full work available at URL: https://doi.org/10.1007/bf01571094
OpenAlex ID: W1997502674
description: scientific article; zbMATH DE number 726950