Stability of N-Fronts Bifurcating from a Twisted Heteroclinic Loop and an Application to the Fitzhugh--Nagumo Equation

In this article, existence and stability of N-front travelling-wave solutions of partial differential equations on the real line is investigated. The N-fronts considered here arise as heteroclinic orbits bifurcating from a twisted heteroclinic loop in the underlying ordinary differential equation describing travelling-wave solutions. It is proved that the N-front solutions are linearly stable provided the fronts building the twisted heteroclinic loop are linearly stable. The result is applied to travelling waves arising in the FitzHugh--Nagumo equation.