Reduction of multidimensional non-linear d'Alembert equations to two-dimensional equations: ansatzes, compatibility of reduction conditions
arXiv:math-ph/0611003
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.
arXiv commentTranslation of the paper to be published in Collection of Papers Dedicated to 70th Anniversary of W.I. Fushchych, Kyiv, Institute of Mathematics, 2006, p. 81-95