The symmetry and some exact solutions of the nonlinear many-dimensional Liouville, d'Alembert and eikonal equations

DOI10.1088/0305-4470/16/15/030zbMath0554.35106OpenAlexW1987201297MaRDI QIDQ3217023

W. I. Fushchich, N. I. Serov

Publication date: 1983

Published in: Journal of Physics A: Mathematical and General (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/3a6ad685d4c7b2662a6c41f9438e346ec2b0aa55

zbMATH Keywords

symmetryLiouville equationd'Alembert equationeikonal equationsinfinitesimal invariance transformations

Mathematics Subject Classification ID

Partial differential equations of mathematical physics and other areas of application (35Q99) Geometric theory, characteristics, transformations in context of PDEs (35A30)

Related Items (19)

Symmetry classification of quasi-linear PDE's containing arbitrary functions ⋮ Symmetry and exact solutions of multidimensional nonlinear wave equations ⋮ Exact solutions of the d'Alembert and Liouville equations in the pseudo- Euclidean space \(R_{2,2}\). I ⋮ Symmetry reduction and some exact solutions of nonlinear biwave equations ⋮ Solutions of the relativistic nonlinear wave equation by solutions of the nonlinear Schrödinger equation ⋮ Particular solutions of the wave equation with cubic nonlinearity in the class of elliptic functions ⋮ New scale-invariant nonlinear differential equations for a complex scalar field ⋮ On subalgebras of the Lie algebra of the extended Poincaré group P̃(1,n) ⋮ Conformally invariant elliptic Liouville equation and its symmetry-preserving discretization ⋮ Reduction of a multidimensional Poincaré-invariant nonlinear equation to two-dimensional equations ⋮ General solutions of the nonlinear wave equation and of the eikonal equation ⋮ On the reduction of the nonlinear multi-dimensional wave equations and compatibility of the d'Alembert-Hamilton system ⋮ Special conformal groups of a Riemannian manifold and Lie point symmetries of the nonlinear Poisson equation ⋮ Subalgebras of the Poincaré algebra AP(2,3) and the symmetric reduction of the nonlinear ultrahyperbolic d'Alembert equation. I ⋮ Preliminary group classification of a class of fourth-order evolution equations ⋮ Conditional and hidden infinite-dimensional symmetries of wave equations ⋮ Nonclassical symmetry reductions of the Boussinesq equation ⋮ A precise definition of reduction of partial differential equations ⋮ Maximal subalgebras of rank n-1 of the algebra AP(1,n) and reduction of nonlinear wave equations. I

This page was built for publication: The symmetry and some exact solutions of the nonlinear many-dimensional Liouville, d'Alembert and eikonal equations