The following results are obtained: 1) \textit{The set ${\mathfrak S}ol(d'A)_n$ of all solutions of the equation ${{\partial^n\log f}\over{\partial x_1\dots\partial x_1}}=0$, ($ n$-d'Alembert equation), ($ n\ge 2$), considered in domains of the $(x^1,\dots,x^n)\in{\mathbb R}^n$, is larger than the set of all functions $ f$ that can be represented in the form $f(x^1,\dots,x^n)=f_1(x^2,\dots,x^n)\dots f_n(x^1,\dots,x^{n-1})$.} 2) \textit{In the set of solutions ${\mathfrak S}ol(d'A)_n$ of the $n$-d'Alembert equation, $(d'A)_n\subset J{\it D}^n({\mathbb R}^n,{\mathbb R})$, there are also some manifolds that have a change of sectional topology (tunneling effect).}