Reduction of the multidimensional d’Alembert equation to two-dimensional equations
We give a classification of the maximal subalgebras of rank $n - 1$ for the extended Poincare algebra $A\bar P (1.n)$, which is realized on the set of solutions of the d'Alembeit equation $\square u + \lambda u^k = 0$. These subalgebras are used for constructing the anzatses reducing this equation to differential equations with two invariant variables.
English version (Springer): Ukrainian Mathematical Journal 46 (1994), no. 6, pp 699-713.
Citation Example: Barannik L. F., Barannyk A. F., Fushchich V. I. Reduction of the multidimensional d’Alembert equation to two-dimensional equations // Ukr. Mat. Zh. - 1994. - 46, № 6. - pp. 651–662.