Exact solutions of reaction-diffusion systems and nonlinear wave equations

We propose a general method to find exact travelling and standing wave solu tions of react ion-diffusion systems and nonlinear wave equations. The meth od is applied to several well-known react ion-diffusion systems such as a c ompetition-diffusion system of Lotka-Volterra type, the Gray-Scott model, a simplification of the Noyes-Field model for the Belousov-Zhabotinskii reac tion, and two- and three-component models for quadratic solitons. We also f ind exact solutions of several generalized nonlinear dispersive equations o ccurring in mathematical physics.