Differential invariants for quasi-linear and semi-linear wave-type equations
type: Item
instance of: scholarly article
title: Differential invariants for quasi-linear and semi-linear wave-type equations
zbMATH Open document ID: 1154.53012
published in: Applied Mathematics and Computation
publication date: 2008-09-01T00:00:00Z
review text: The quasi-linear wave equation \(u_{tt}=f(t,x,u)u_{xx}+g(t,x,u,u_t,u_x)\) is investigated by group-theoretic method. The authors derive some differential invariants for a class of the equations of the above type, and use them to give a linearization test, i.e. solving equivalence with simplest linear hyperbolic or elliptic equations.
Mathematics Subject Classification ID: 53A55
Mathematics Subject Classification ID: 35A30
Mathematics Subject Classification ID: 35L05
zbMATH DE Number: 5318711
zbMATH Keywords: wave equation
zbMATH Keywords: equivalence transformation
zbMATH Keywords: differential invariant
zbMATH Keywords: linearization
author: Christodoulos Sophocleous
author: R. Tracinà
reviewed by: Boris Kruglikov
MaRDI profile type: Publication
full work available at URL: j.amc.2008.01.033
OpenAlex ID: W1992992229
cites work: Q4222370
cites work: On invariance properties of the wave equation
cites work: Q3966539
cites work: An analogue of the Moutard transformation for the Goursat equation \(\vartheta_{xy}=2\sqrt{\lambda(x,y)\vartheta_x\vartheta_y}\)
cites work: Preliminary group classification of equations v t t=f (x,v x)v x x+g(x,v
cites work: Q4357207
cites work: Laplace type invariants for parabolic equations
cites work: Invariants of a remarkable family of nonlinear equations
cites work: Differential invariants of nonlinear equations \(v_{tt}=f(x,v_{x})v_{xx}+g(x,v_{x})\).
cites work: Differential invariants of the one-dimensional quasi-linear second-order evolution equation
cites work: Q5476892
cites work: Q4812015
cites work: Linearization of third-order ordinary differential equations by point and contact transformations
cites work: Singular invariant equation for the \((1+1)\) Fokker-Planck equation.
cites work: Many-parameter solutions of the Tzitzéica equation
cites work: Q3732104
cites work: Q4849745
cites work: Q3945260
cites work: On the linearization of semilinear wave equations
cites work: Second-order differential invariants of a family of diffusion equations
cites work: Invariants of a family of nonlinear wave equations.
cites work: The sine-Gordon equations: Complete and partial integrability
cites work: Q4151274
cites work: Exactly integrable hyperbolic equations of Liouville type
DOI: 10.1016/J.AMC.2008.01.033
description: scientific article; zbMATH DE number 5318711