Existence and Stability of Traveling Pulses in a Reaction-Diffusion-Mechanics System

In this article, we analyze traveling waves in a reaction–diffusionmechanics (RDM) system. The system consists of a modified FitzHugh–Nagumo equation, also known as the Aliev–Panfilov model, coupled bidirectionally with an elasticity equation for a deformable medium. In one direction, contraction and expansion of the elastic medium decreases and increases, respectively, the ionic currents and also alters the diffusivity. In the other direction, the dynamics of the R–D components directly influence the deformation of the medium. We demonstrate the existence of traveling waves on the real line using geometric singular perturbation theory. We also establish the linear stability of these traveling waves using the theory of exponential dichotomies.