Traveling waves in reaction-diffusion system: diffusion with finite velocity and Kolmogorov-Petrovskii-Piskunov kinetics
نویسنده
چکیده
A new asymptotic method is presented for the analysis of the traveling waves in the onedimensional reaction-diffusion system with the diffusion with a finite velocity and KolmogorovPetrovskii-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. PACS numbers: 05.70.Ln, 82.20.Db
منابع مشابه
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...
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