Reduction of multi-dimensional d'Alembert equations to two-dimensional equations: ansatzes, compatibility of the reduction conditions, reduced equations

Abstract

We study conditions of reduction of multidimensional wave equations - of a system of d'Alembert and Hamilton equations. Necessary conditions for compatibility of such reduction conditions are proved. Possib\-le 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.