Reduction of non-linear d'Alembert equations to two-dimensional equations

Details Reduction of non-linear d'Alembert equations to two-dimensional equations Reduction of non-linear d'Alembert equations to two-dimensional equations

2009-10-14

arxiv.org/abs/0910.2501v1

Proceedings of the 4th Workshop "Group Analysis of Differential Equations & Integrable Systems", 2009, p. 243-253

Physics

Mathematical Physics

The published paper with some mistakes corrected

Scientific paper

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.

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