Similarity reductions and similarity solutions for the generalized diffusion equation

Abstract

Herein, the generalized diffusion equation that encompasses the nonlinear diffusion equation with a source term and the Boussinesq equation in hydrology as its particular form and appears in a wide variety of physical and engineering applications has been analyzed via symmetry method that was developed by Steinberg. According to physical situations, in each case, the similarity variables obtained have led us to an ordinary differential equation, and we acquire some new solutions by solving the ODEs. Copyright © 2015 John Wiley & Sons, Ltd