Some new solitary and travelling wave solutions of certain nonlinear diffusion–reaction equations using auxiliary equation method

Attempts are made to look for the soliton content in the exact solutions of certain types of nonlinear diffusion–reaction (DR) equations with the quadratic and cubic nonlinearities. Such equations may arise in a variety of contexts in physical problems. In this Letter using the auxiliary equation method, some new solitary and travelling wave solutions of such nonlinear DR equations are obtained in a very general form. Several interesting special cases of these general solutions are also discussed.