Accurate computation of traveling wave solutions of some nonlinear diffusion equations

We consider a class of degenerate diffusion reaction equations where the nonlinearity is assumed to be singular at zero. We carry out a traveling wave analysis for these equations showing the existence of different types of traveling wave solutions, in particular, sharp type solution with minimum speed. We use two different methods for the numerical computation of such wave solutions for a special case of these equations. One of the methods involve the traveling wave equations and leads to accurate computation of wave profiles and speeds. The second method is to solve an initial-boundary-value problem with an adaptive traveling wave condition for the partial differential equation.