Exact solutions of variable coefficient nonlinear diffusion–reaction equations with a nonlinear convective term

Attempts have been made to look for the exact solutions of certain types of nonlinear diffusion–reaction equations which involve not only the quadratic and quartic nonlinearities but also a time-dependent nonlinear convective flux term. In particular, the solitary wave solutions are found. Such equations arise in a variety of contexts in physical and biological problems.