Solitary Wave Dynamics Governed by the Modified FitzHugh–Nagumo Equation

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.