  We study conditions of reduction of the multidimensional wave equation - a
system of the d'Alembert and Hamilton equations. We prove necessary conditions
for compatibility of such system of the reduction conditions. Possible types of
the reduced equations represent interesting classes of two-dimensional
parabolic, hyperbolic and elliptic equations. Ansatzes and methods used for
reduction of the d'Alembert (n-dimensional wave) equation can be also used for
arbitrary Poincare-invariant equations. This seemingly simple and partial
problem involves many important aspects in the studies of the PDE.
