Wave front for a reaction-diffusion system and relativistic Hamilton-Jacobi dynamics

The problem of wave-front propagation for the n-dimensional reaction-diffusion system involving Kolmogorov-Petrovskii-Piskunov kinetics and the diffusion transport with a finite velocity has been considered. By using a scaling procedure we have given an asymptotic derivation of the equation governing the evolution of a reaction front in the long-time large-distance limit. It has been found that this equation is identical in form to the relativistic Hamilton-Jacobi equation. In the case of a constant value of chemical rate function we have derived exact formulas for the position of reaction front and the speed of propagation by using relativistic mechanics techniques.