New results on group classification of nonlinear diffusion-convection equations

Abstract:
Using a new method and transformations Using a new method and transformations of conditional equivalence, we carry out group classification in a class of variable coefficient (1+1)-dimensional nonlinear diffusion-convection equations of the general form f(x)u_t = (D(u)u_x)_x+K(u)u_x. We obtain new interesting cases of such equations with localized density f, having large invariance algebra. Examples of Lie ansatze and exact solutions of these equations are constructed.

The talk is based on our work math-ph/0306035.