Exact solutions for Belousov-Zhabotinskii reaction-diffusion system

We consider the following simplified model for the Belousov-Zhabotinskii (B-Z) reaction: $left{ {mathop {}limits_{frac{{partial u}}{{partial t}} = - suv + dfrac{{partial ^2 u}}{{partial x^2 }}, }^{frac{{partial u}}{{partial t}} = - u(1 - u - rv) + dfrac{{partial ^2 u}}{{partial x^2 }},} } right.$ wherer ands are positive parameters, andd is the diffusing constant for the concentrationu. Seeking travelling wave front solution and making an ansatz for the solution, we obtain a nonlinear system of algebraic equations. The system is solved using Wu Elimination and then we are able to find several exact solutions which are of interest.