PAINLEVE TEST AND EXACT SIMILARITY SOLUTIONS OF A CLASS OF NONLINEAR DIFFUSION-EQUATIONS

For (1+1)-dimensional diffusion equations where the diffusion coefficient is an arbitrary power of the dependent variable, a Painleve test is performed on both the partial differential equation and the similarity reductions. The invariance of the Painleve property under a large class of similarity reductions is shown. For the reductions with the Painleve property, the explicit similarity solutions are given. It is demonstrated how results of a Painleve analysis can be used to obtain further exact similarity solutions, even in cases without the Painleve property.