Abstract
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).