A potential constraints method of finding nonclassical symmetry of PDEs based on Wu's method
type: Item
instance of: scholarly article
title: A potential constraints method of finding nonclassical symmetry of PDEs based on Wu's method
zbMATH Open document ID: 1442.35015
DOI: 10.1155/2019/9272347
author: Tonglaga Bai
author: Temuer Chaolu
published in: Advances in Mathematical Physics
publication date: 2020-07-16T00:00:00Z
review text: Summary: Solving nonclassical symmetry of partial differential equations (PDEs) is a challenging problem in applications of symmetry method. In this paper, an alternative method is proposed for computing the nonclassical symmetry of PDEs. The method consists of the following three steps: firstly, a relationship between the classical and nonclassical symmetries of PDEs is established; then based on the link, we give three principles to obtain additional equations (constraints) to extend the system of the determining equations of the nonclassical symmetry. The extended system is more easily solved than the original one; thirdly, we use Wu's method to solve the extended system. Consequently, the nonclassical symmetries are determined. Due to the fact that some constraints may produce trivial results, we name the candidate constraints as ``potential'' ones. The method gives a new way to determine a nonclassical symmetry. Several illustrative examples are given to show the efficiency of the presented method.
Mathematics Subject Classification ID: 35B06
Mathematics Subject Classification ID: 35G20
zbMATH DE Number: 7221715
zbMATH Keywords: potential constraints
zbMATH Keywords: classical and nonclassical symmetries
Wikidata QID: Q114070453
describes a project that uses: GeM
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2019/9272347
OpenAlex ID: W2960938181
cites work: Symmetries and differential equations
cites work: Q4273954
cites work: Q5581041
cites work: Q4876472
cites work: Reduction operators of linear second-order parabolic equations
cites work: Conditional symmetries for systems of PDEs: new definitions and their application for reaction–diffusion systems
cites work: On the weak symmetry groups of partial differential equations
cites work: Nonclassical symmetry reductions of the Boussinesq equation
cites work: Applications of nonclassical symmetries
cites work: Nonclassical symmetry reductions of the linear diffusion equation with a nonlinear source
cites work: Direct reduction and differential constraints
cites work: CRC Handbook of Lie Group Analysis of Differential Equations, Volume I
cites work: Bogus transformations in mechanics of continua
cites work: Potential symmetries and direct reduction methods of order two
cites work: Evolution equations, invariant surface conditions and functional separation of variables
cites work: GeM software package for computation of symmetries and conservation laws of differential equations
cites work: Reduction of systems of nonlinear partial differential equations to simplified involutive forms
cites work: Involution and symmetry reductions
cites work: Algorithms for the Nonclassical Method of Symmetry Reductions
cites work: Q4937603
cites work: Q5017572
cites work: Nonclassical potential solutions of partial differential equations
cites work: An algorithm for the complete symmetry classification of differential equations based on Wu's method
cites work: An algorithmic method for showing existence of nontrivial non-classical symmetries of partial differential equations without solving determining equations
cites work: Q2716051
cites work: Q4713581
cites work: Associative differential operations
cites work: Q4798728
cites work: Non-classical symmetry reduction: example of the Boussinesq equation
cites work: New similarity reductions of the Boussinesq equation
cites work: Lump solutions to the Kadomtsev-Petviashvili equation
description: scientific article; zbMATH DE number 7221715