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Reduction of multidimensional non-linear d'Alembert equations to two-dimensional equations: ansatzes, compatibility of reduction conditions

Irina Yehorchenko
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Abstract

We study conditions of reduction of multidimensional wave equations - a system of d'Alembert and Hamilton equations. Necessary conditions for compatibility of such reduction conditions are proved. Possible types of the reduced equations and ansatzes are described. We also provide a brief review of the literature with respect to compatibility of the system of d'Alembert and Hamilton equations and construction of solutions for the nonlinear d'Alembert equation.

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Irina Yehorchenko. 2006-11-01. Reduction of multidimensional non-linear d'Alembert equations to two-dimensional equations: ansatzes, compatibility of reduction conditions. https://arxiv.org/abs/math-ph/0611003

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