Generalized separation of variable for nonlinear equation utt=a(t)uxx+b(t)u2x+c(t)uutt=a(t)uxx+b(t)ux2+c(t)u

Abstract

We propose a generalized procedure of separation of variables for nonlinear equations and construct broad classes of exact solutions of these equations that cannot be obtained by the classical Lie method and the method of conditional symmetries.