JAMC J Appl Math Comput (2011) 35: 93–102 DOI 10.1007/s12190-009-0344-4 New exact solutions for some power law nonlinear diffusion equation Olawanle P. Layeni Received: 7 May 2009 / Published online: 10 October 2009 © Korean Society for Computational and Applied Mathematics 2009 Abstract An extended auxiliary equation method for exact traveling wave solutions of constant coefficient nonlinear partial differential equations of evolution is pro- posed. This, together with a convenient characterization, affords new exact traveling wave solutions of some classes of nonlinear power law diffusion equations to be ob- tained. Keywords Auxiliary equation method · Traveling waves · Nonlinear Diffusion Equation Mathematics Subject Classification (2000) 35K57 · 35Q51 1 Introduction In this article we study the nonlinear diffusion equation u t − eu xx − du δ u x − ru β − su γ = 0, (1) δ ≥ 0, γ ≥ β , with e,d,r,s being nonzero constants, for its exact traveling wave (TW) solutions. It is observed that under a transform u(x,t)  → u μ (x,t),(1) bears a direct relationship with the generalized Burgers-Fisher equation u t − du μδ u x − e(μ − 1) u x u − eu xx − r μ u β ⋆ − s μ u γ ⋆ = 0, (2) O.P. Layeni ( ) Department of Mathematics, Obafemi Awolowo University, Ile-Ife 220005, Nigeria e-mail: olawanle.layeni@gmail.com O.P. Layeni e-mail: olayeni@oauife.edu.ng