An algorithm for the complete symmetry classification of differential equations based on Wu's method
type: Item
instance of: scholarly article
title: An algorithm for the complete symmetry classification of differential equations based on Wu's method
zbMATH Open document ID: 1204.35021
author: Temuer Chaolu
author: Pang Jing
published in: Journal of Engineering Mathematics
publication date: 2010-06-16T00:00:00Z
review text: An alternative algorithm using Wu's method (differential characteristic set algorithm) is proposed for complete symmetry classification of partial differential equations involving arbitrary parameters. Such classification is determined by decomposing the solution set of the determining equations into a union of a series of zero sets of differential characteristic sets of the corresponding differential polynomial system. Each branch of the resulting decomposition yields a class of symmetries and the corresponding parameters. The proposed algorithm makes the classification direct and systematic, which also provides a novel application of Wu's method to differential equations. To show the efficiency of the algorithm, complete potential symmetry classifications are given for linear and nonlinear wave equations with an arbitrary function parameter and both classical and nonclassical symmetries of a parametric Burgers equation as illustrative examples.
Mathematics Subject Classification ID: 35B06
Mathematics Subject Classification ID: 35A30
Mathematics Subject Classification ID: 58J70
Mathematics Subject Classification ID: 35K05
Mathematics Subject Classification ID: 58J72
Mathematics Subject Classification ID: 35A25
zbMATH DE Number: 5721527
zbMATH Keywords: Lie symmetries
zbMATH Keywords: differential characteristic set algorithm
zbMATH Keywords: parametric differential equations
zbMATH Keywords: linear wave equations
zbMATH Keywords: nonlinear wave equations
zbMATH Keywords: parametric Burgers equation
reviewed by: Wen-Xiu Ma
describes a project that uses: SYMMGRP
describes a project that uses: diffgrob2
MaRDI profile type: Publication
full work available at URL: s10665-009-9344-5
OpenAlex ID: W1965553298
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DOI: 10.1007/S10665-009-9344-5
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description: scientific article; zbMATH DE number 5721527