Uncountable Infinite Exact Solutions to the FitzHugh-Nagumo Model

TL;DR

This paper reports the discovery of uncountably infinite exact solutions to the FitzHugh-Nagumo model using non-classical symmetry analysis, significantly advancing the understanding of this nonlinear system across various scientific fields.

Contribution

It presents the first known uncountable set of exact solutions to the FitzHugh-Nagumo model, eliminating the need for asymptotics or numerics for certain analyses.

Findings

Found uncountable infinite exact solutions

Solutions are physically stable and meaningful

Obsoletes many previous asymptotic and numerical methods

Abstract

First time in six decades, uncountable infinite exact solutions of FitzHugh-Nagumo model with diffusion have been found. FitzHugh-Nagumo model is a nonlinear dynamical system applicable to neurosciences, chemical kinetics, cell division, population dynamics, electronics, epidemiology, cardiac physiology and pattern formation. Non-classical symmetry analysis has been carried out to find invariant solutions. In many ways this finding makes the corpus of asymptotics and numerics obsolete. Non singular, physically stable and meaningful solutions could now be found without distorting the actual model or introducing forced conditions.