# Traveling waves in reaction-diffusion system

Source: [Traveling waves in reaction-diffusion system](<https://www.sota2.com/research/paper/68fa1e9c7a2b558e29323823>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-23T15:28:16.665Z

Authors: Sergei Fedotov

Published: 1998-07-27T13:32:01.000Z

## 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.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/cond-mat/9807352>)

[PDF](<https://arxiv.org/pdf/cond-mat/9807352.pdf>)