Exact solutions of reaction-diffusion systems and nonlinear wave equations
We propose a general method to find exact travelling and standing wave solutions of reaction-diffusion systems and nonlinear wave equations. The method is applied to several well-known reaction-diffusion systems such as a competition-diffusion system of LotkaVolterra type, the Gray-Scott model, a simplification of the Noyes-Field model for the Belousov-Zhabotinskii reaction, and two- and three-component models for quadratic solitons. We also find exact solutions of several generalized nonlinear dispersive equations occurring in mathematical physics.
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