Mathematics

Critical travelling waves in one model of the "reaction-diffusion" type

V. A. Sobolev^a, E. A. Tropkina^a, E. A. Shchepakina^a, L. Zhang^b, J. Wang<sup>b

a</sup> Samara National Research University, Samara, Russian Federation
^b Shandong University of Science and Technology, Qingdao, Shandong, China

Abstract: The paper is devoted to the order reduction for critical traveling wave problems for a reaction-diffusion type systems. The mathematical apparatus is based on the geometric theory of singular perturbations and the canards technique. The use of the method of invariant manifolds of singularly perturbed systems allows us to replace the study of traveling waves of the original PDE system by analyzing their profiles in a ODE system of a lower order.

Keywords: singular perturbations, slow invariant manifolds, critical travelling waves, singular perturbations, integral manifold, order reduction, asymptotic expansion, differential equations, fast variables, slow variables.

UDC: 517.928

Received: 18.03.2020
Revised: 20.04.2021
Accepted: 28.05.2021

DOI: 10.18287/2541-7525-2021-27-2-16-24