Linearizing mappings for certain nonlinear diffusion equations

Abstract

In this paper we consider the nonlinear diffusion equations of the type ut = x1-M[xN-1λ(u + u)-2ux]x. It is shown that linearizing point transformations do not exist. This equation can be equivalently written as a system of two and three equations, respectively. Linearizing point transformations are sought for these two auxiliary systems and the complete list is presented. These in turn may be employed to construct contact transformations which map the nonlinear diffusion equation to a linear partial differential equation. Such linearizing point transformations exist only if N = 2 - M and N = 2 + M.