Loop algebra of Lie symmetries for a short-wave equation
type: Item
instance of: scholarly article
title: Loop algebra of Lie symmetries for a short-wave equation
zbMATH Open document ID: 0648.58042
DOI: 10.1007/BF00672047
author: S. Roy
author: A. Roy Chowdhury
author: Mrityunjoy De
published in: International Journal of Theoretical Physics
publication date: 1988-01-01T00:00:00Z
review text: This paper deals with symmetry transformations of the nonlinear differential equation \[ 2\cdot K\cdot \Phi_ x+\Phi_{yy}+2\cdot \Phi_{xt}-2\cdot (x+\Phi_ x)\cdot \Phi_{xx}=0 \] of short waves. The Lie algebra of symmetries is discussed and characterized in connection to the loop or Virasoro algebra, its structure is given by a tensor product of a finite-dimensional part and the space \(L(t,t^{-1})\) of Laurent polynomials. Using the adjoint representation to form special generators, solutions generated by the corresponding transformations are constructed.
Mathematics Subject Classification ID: 58J72
Mathematics Subject Classification ID: 17B65
Mathematics Subject Classification ID: 35C05
Mathematics Subject Classification ID: 35Q99
zbMATH DE Number: 4058495
zbMATH Keywords: infinite-dimensional Lie algebra
zbMATH Keywords: closed-form solutions
zbMATH Keywords: loop algebra
zbMATH Keywords: Virasoro algebra
Wikidata QID: Q115394963
reviewed by: Günter Czichowski
MaRDI profile type: Publication
cites work: Similarity methods for differential equations
cites work: Q3693672
description: scientific article; zbMATH DE number 4058495