Reduction of non-linear d'Alembert equations to two-dimensional equations
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Publication:3006827
zbMATH Open1227.35187arXiv0910.2501MaRDI QIDQ3006827
Publication date: 21 June 2011
Abstract: We study conditions of reduction of the multidimensional wave equation - a system of the d'Alembert and Hamilton equations. We prove necessary conditions for compatibility of such system of the reduction conditions. Possible types of the reduced equations represent interesting classes of two-dimensional parabolic, hyperbolic and elliptic equations. Ansatzes and methods used for reduction of the d'Alembert (n-dimensional wave) equation can be also used for arbitrary Poincare-invariant equations. This seemingly simple and partial problem involves many important aspects in the studies of the PDE.
Full work available at URL: https://arxiv.org/abs/0910.2501
Related Items (3)
On the reduction of the nonlinear multi-dimensional wave equations and compatibility of the d'Alembert-Hamilton system ⋮ Reduction of a multidimensional poincare-invariant nonlinear equation to two-dimensional equations ⋮ On Reduction of the Euler Equations by Means of Two-Dimensional Algebras
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