Symmetry groups and separation of variables of a class of nonlinear diffusion-convection equations

In this paper, a class of nonlinear diffusion-convection equations, u t = ( D ( u ) u x n ) x + P ( u ) u x , which has quite a large number of physical applications, is analysed by using symmetry group methods which include the classical method, the potential symmetry method and the generalized conditional symmetry method. A complete classification of the functional forms of the diffusion and convection coefficients is presented when the equation admits Lie's point symmetry groups and potential symmetry groups. The separation of variables for the equation is investigated using the generalized conditional symmetry approach. For some interesting cases, exact solutions using the method of separation of variables are discussed in detail.