# Solitary wave dynamics governed by the modified FitzHugh-Nagumo equation

## TL;DR

This paper investigates the solitary wave solutions of the modified FitzHugh-Nagumo system, revealing two types with different velocities, analyzing their stability, and exploring their formation and annihilation mechanisms.

## Contribution

It demonstrates the existence of two soliton-type solutions with distinct velocities and provides a detailed stability analysis using numerical and Evans function techniques.

## Key findings

- Fast solitary waves are stable.
- Slow solitary waves are unstable.
- Formation and annihilation of localized regimes are discussed.

## Abstract

The paper deals with the studies of the nonlinear wave solutions supported by the modified FitzHugh-Nagumo (mFHN) system. It was proved in our previous work that the model, under certain conditions, possesses a set of soliton-like traveling wave (TW) solutions. In this paper we show that the model has two solutions of the soliton type differing in propagation velocity. Their location in parametric space, and stability properties are considered in more details. Numerical results accompanied by the application of the Evans function technique prove the stability of fast solitary waves and instability of slow ones. A possible way of formation and annihilation of localized regimes in question is studied therein too.