Exact travelling wave solutions for a diffusion-convection equation in two and three spatial dimensions

The modified extended tanh-function method were applied to the general class of nonlinear diffusion-convection equations where the concentration-dependent diffusivity, D(u), was taken to be a constant while the concentration-dependent hydraulic conductivity, K(u) were taken to be in a power law. The obtained solutions include rational-type, triangular-type, singular-type, and solitary wave solutions. In fact, the profile of the obtained solitary wave solutions resemble the characteristics of a shock-wave like structure for an arbitrary m (where m>1 is the power of the nonlinear convection term).