On the set of solutions of the generalized d'Alembert equation

The following results are been obtained: 1) The set Sol(d'A)(n) of all solu tions of the equation partial derivative(n) log f/partial derivative x(n) . .. partial derivative x(1) = 0, (n-d'Alembert equation), (n greater than or equal to 2), considered in domains of the (x(1),...,x(n)) is an element of R-n, is larger than the set of all functions f that can be represented in the form (sic), f(x(1),...,x(n)) = f(1)(x(2);x(3),...,x(n))... f(n) (x(1),x (2),..., x(n-1)). 2) In the set of solutions Sol(d'A)(n) of the n-d'Alember t equation, (d'A)(n) subset of JD(n)(R-n,R), there are also some manifolds that have a change of sectional topology (tunneling effect). (C) Academie d es Sciences/Elsevier. Paris.