An analysis of the nonlinear equation $u_{t} = f(x, u) u_{xx} + g(x, u) u_{x}^{2} + h(x, u) u_{x} + p(x, u)$

Abstract

We use the method of preliminary group classification to analyse a particular form of the nonlinear diffusion equation in which the inhomogeneity is quadratic in u x . The method yields an optimal system of one-dimensional subalgebras. As a result we obtain those explicit forms of the unknown functions f, g, h and p for which the equation admits additional point symmetries.