Nonclassical Potential System Approach for a Nonlinear Diffusion Equation

Abstract

In this paper we consider a class of equations that model diffusion. For some of these equations nonclassical potential symmetries are derived by using a modified system approach. These symmetries allow us to increase the number of exact known solutions. These solutions are unobtainable from classical potential symmetries derived by using the so called natural potential system nor from nonclassical symmetries of the given partial differential equation.