A CLASS OF SPECIAL EXACT SOLUTIONS OF SOME HIGH DIMENSIONAL NON-LINEAR WAVE EQUATIONS

Abstract

In this paper, the separation transformation approach is extended to some high dimensional non-linear wave equations, such as the (N+1)-dimensional Zhiber–Shabat equation, the generalized (N+1)-dimensional complex non-linear Klein–Gordon equation and the generalized (N+1)-dimensional Toda lattice equation. As a result, a class of special exact solutions of these equations are obtained. The solutions obtained contain one or two arbitrary functions which may lead to abundant structures of the high dimensional non-linear wave equations.