On a sequence of higher-order nonlinear diffusion-convection equations

Abstract

Motivated by the existence of the thin film equations, fourth and sixth order, which are generalizations of the diffusion equation, we consider a sequence of higher order nonlinear diffusion-convection equations. We investigate this class of nonlinear equations from the point of view of Lie group analysis. In particular, we derive Lie symmetries, potential symmetries, nonclassical reductions and potential nonclassical reductions for a third and a fourth equation. The present work is a motivation for further investigation on this sequence of nonlinear partial differential equations. Certain general results of higher order equations of the sequence are given.