Complete and exact solutions of a class of nonlinear diffusion equations and problem of velocity selection

In this Rapid Communication complete and exact solutions of a class of nonlinear diffusion equations have been presented. The exact solutions give a tutorial explanation about the mechanism of velocity selection. The marginal stability hypothesis is extended to predict velocity selection for the equations. It has been shown that this class of equations can be transformed to the heat equation via nonlinear transformations. Numerical experiments have been performed to test the theoretical prediction.