The objective of this article is the generalization of the homogeneous reaction-diffusion equations of the monostable or bistable types. ¶From the non-linear second order differential equation of the front profile (solution of the homogeneous reaction-diffusion equations), a method of generalization of the homogeneous reaction-diffusion equations, based on the theory of factorization of ordinary differential operators [9], was proposed. This method enables us to build two generalized homogeneous reaction-diffusion equations: the first with one species and the second with two species.

homogeneous reaction-diffusion equations, method of factorization of ordinary differential operators, population dynamics.