Generalized separation of variables for nonlinear equationutt = F(u)uxx + aF′(u)u2х

Abstract

Where F(u), a#0 are an arbitrary function and constant, correspondingly. The problem is studied for which functions F(u) it admits ans¨atz t = w1(x)d(u) + w2(x), which reduces this equation to a system of two ordinary differential equations with unknown functions w1(x) and w2(x). For these equations classes of exact solutions with generalized separation of variables are constructed, which can not be obtained by the method of classical group analysis.