Kink wave and saddle-spiral shock wave of a partial differential equation model of excitable media

In this paper, traveling waves of a PDE model of excitable media are investigated. Traveling wave system of the model can be treated as a singular perturbation system in R3R3. By the dynamical system method and geometric singular perturbation theory, we prove that there exist two manifolds in R3R3 intersecting along a one-dimensional curve which exactly corresponds to a monotone kink wave or a saddle-spiral shock wave of the PDE model.