Solitary waves in the model of active media, taking into account relaxing effects

TL;DR

This paper investigates solitary wave solutions in a generalized FitzHugh-Nagumo model that incorporates memory effects due to internal structure, providing explicit solutions and stability analysis relevant to active media.

Contribution

It introduces a generalized model including memory effects and explicitly constructs and analyzes the stability of localized traveling wave solutions.

Findings

Explicit solitary wave solutions are constructed.

Stability of these solutions is analyzed.

The model extends classical nerve impulse models with internal memory effects.

Abstract

We study a system of differential equation simulating transport phenomena in active structured media. The model is a generalization of the McKean s modification of the celebrated FitzHugh--Nagumo system, describing the nerve impulse propagation in axon. It takes into account the effects of memory, connected with the presence of internal structure. We construct explicitly the localized traveling wave solutions and analyze their stability.