Classification and reduction of some systems of quasilinear partial differential equations
type: Item
instance of: scholarly article
title: Classification and reduction of some systems of quasilinear partial differential equations
zbMATH Open document ID: 0961.35005
DOI: 10.1016/S0362-546X(98)00351-4
author: Qu Changzheng
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2001-05-15T00:00:00Z
review text: By the generalized conditional symmetry (GCS) method of Fokas and Liu the author investigates a class of systems of quasilinear partial differential equations (PDEs), which have applications in many areas of science and engineering. Reduction to systems of ordinary differential equations (ODEs) is made under GCS: \(\{ \sigma_1 , \sigma_2 \} = \{ u_{xxx} \pm u_{x} , v_{xxx} \pm v_{x} \}\) and \( \{ \sigma_1 , \sigma_2 \} = \{ u_{xxx} , v_{xxx} \}\). The relationship of the GCS method and the approach of invariant linear subspaces is analyzed. For systems of quasilinear hyperbolic PDEs exact solutions and reductions to ODE are constructed. There are considered three particular cases. For an illustration of the GCS method the author presents the following examples: parabolic system of equations with source and absorption; a system with quadratic nonlinearities; a system with nonlinear connection terms. Finally, explicit exact solutions are obtained.
reviewed by: Violeta Tretynyk
Mathematics Subject Classification ID: 35A25
Mathematics Subject Classification ID: 34C14
Mathematics Subject Classification ID: 35C05
Mathematics Subject Classification ID: 58J70
zbMATH DE Number: 1491654
zbMATH Keywords: exact solution and reduction
zbMATH Keywords: generalized conditional symmetry
MaRDI profile type: Publication
full work available at URL: s0362-546x(98)00351-4
OpenAlex ID: W2021557835
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description: scientific article; zbMATH DE number 1491654