Existence of the solitary wave solutions supported by the hyperbolic modification of the FitzHugh-Nagumo system

TL;DR

This paper investigates a generalized FitzHugh-Nagumo system, demonstrating the existence of soliton-like solutions through theoretical analysis and numerical simulations, advancing understanding of nerve impulse modeling.

Contribution

It introduces a hyperbolic modification of the FitzHugh-Nagumo system and proves the existence of solitary wave solutions under specific parameter conditions.

Findings

Existence of soliton-like solutions in the modified system

Theoretical validation supported by numerical simulations

Conditions on parameters for soliton existence

Abstract

We study a system of nonlinear differential equations simulating transport phenomena in active media. The model we are interested in is a generalization of the celebrated FitzHugh-Nagumo system, describing the nerve impulse propagation in axon. The modeling system is shown to possesses soliton-like solutions under certain restrictions on the parameters. The results of theoretical studies are backed by the direct numerical simulation.