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