Gianni Arioli, Hans Koch Existence and stability of traveling pulse solutions of the FitzHugh-Nagumo equation (1086K, plain TeX, with eps figures) ABSTRACT. The FitzHugh-Nagumo model is a reaction-diffusion equation describing the propagation of electrical signals in nerve axons and other biological tissues. One of the model parameters is the ratio ε of two time scales, which takes values between 0.001 and 0.1 in typical simulations of nerve axons. Based on the existence of a (singular) limit at ε=0, it has been shown that the FitzHugh-Nagumo equation admits a stable traveling pulse solution for sufficiently small ε>0. In this paper we prove the existence of such a solution for ε=0.01. We consider both circular axons and axons of infinite length. Our method is non-perturbative and should apply to a wide range of other parameter values.