Traveling waves in reaction-diffusion system

TL;DR

This paper introduces a novel asymptotic method combining path-integral, scaling, and large deviations techniques to analyze traveling waves in reaction-diffusion systems with finite velocity diffusion, deriving exact front position and speed formulas.

Contribution

It presents a new analytical approach for reaction-diffusion traveling waves, linking front dynamics to relativistic mechanics, and provides exact formulas for front position and speed.

Findings

Exact formulas for reaction front position and speed.

Reaction front dynamics related to relativistic Hamiltonian mechanics.

Method applicable to systems with finite velocity diffusion.

Abstract

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.