Stability of Traveling Wavefronts for the Discrete Nagumo Equation

Abstract

It has been shown that the discrete Nagumo equation \[ \dot u_n = d(u_{n - 1} - 2u_n + u_{n + 1} ) + f(u_n ),\quad n \in \mathbb{Z},\], has a traveling wavefront solution for sufficiently strong coupling d. In this paper it is shown that such a traveling wavefront is unique (up to a shift in time) and globally stable.