  A new asymptotic method is presented for the analysis of the traveling waves
in the one-dimensional reaction-diffusion system with the diffusion with a
finite velocity and Kolmogorov-Petrovskii-Piskunov kinetics. The analysis makes
use of the path-integral approach, scaling procedure and the singular
perturbation techniques involving the large deviations theory for the Poisson
random walk. The exact formula for the position and speed of reaction front is
derived. It is found that the reaction front dynamics is formally associated
with the relativistic Hamiltonian/Lagrangian mechanics.
