Preliminary group classification of the nonlinear differential-difference equations
type: Item
instance of: scholarly article
title: Preliminary group classification of the nonlinear differential-difference equations
zbMATH Open document ID: 1267.34062
author: Yang Cong
author: Xiaoling Zhang
author: Hong-Qing Zhang
published in: Journal of Mathematical Analysis and Applications
publication date: 2013-01-24T00:00:00Z
review text: Combining Lie's infinitesimal method and the theory of the classification of abstract finite-dimensional Lie algebras, the authors give a preliminary group classification of the nonlinear differential-difference equation \[ \Delta_n\equiv\ddot{u}_n(t)-F_n(t, u_{n-1}(t), u_n(t), u_{n+1}(t))=0. \] It is proved that there exists only one equation admitting three-dimensional simple Lie algebras, and there exist 3, 11, 22, 13 inequivalent equations admitting one-, two-, three- and four-dimensional solvable Lie algebras, respectively. Also, there exist two inequivalent equations admitting five- and seven-dimensional indecomposable algebras of semi-direct sums of semi-simple and solvable Lie algebras. It should be mentioned, that this classification is incomplete and that it is not possible to give a complete group classification within the presented framework.
reviewed by: Oleg V. Makeev
Mathematics Subject Classification ID: 34C14
zbMATH DE Number: 6128649
zbMATH Keywords: preliminary group classification
zbMATH Keywords: nonlinear differential-difference equations
zbMATH Keywords: Lie algebra
MaRDI profile type: Publication
full work available at URL: j.jmaa.2012.10.046
OpenAlex ID: W1977851070
DOI: 10.1016/J.JMAA.2012.10.046
description: scientific article; zbMATH DE number 6128649