On point transformations of generalized nonlinear diffusion equations

Abstract

This paper classifies all finite point transformations of a general class between generalized diffusion equations of the form ut=x 1-M [xN-1f(u)ux]x. These transformations may be divided into three cases, depending on the functional form of f(u): (i) f arbitrary, (ii) f=un and (iii) f=eu. In particular, these transformations include all the invariant infinitesimal transformations and, in addition, they include a number of point transformations which relate different equations of the above form. Many exact solutions are already known and the transformations which are derived may be used to obtain new solutions from these.