Reduction of the multidimensional d’Alembert equation to two-dimensional equations
We give a classification of maximal subalgebras of rankn?1 for the extended Poincaré algebra\(A\bar P (1.n)\), which is realized on the set of solutions of the d'Alembert equation\(\square u + \lambda u^k = 0\). These subalgebras are used for constructing anzatses that reduce 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 A. F., Barannik L. F., Fushchich V. I. Reduction of the multidimensional d’Alembert equation to two-dimensional equations // Ukr. Mat. Zh. - 1994. - 46, № 6. - pp. 651–662.