  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.
