On the Invariant Solutions of Some Five-Dimensional D’alembert Equations

Abstract

By using the invariants of nonconjugate subgroups of the Poincaré group P(1,4) [conjugation is considered with respect to the group P(1,4)], we propose ansatzes that reduce some linear and nonlinear five-dimensional d’Alembert equations to ordinary differential equations. On the basis of the solutions of the reduced equations, we construct the invariant solutions of these five-dimensional d’Alembert equations.