A topological proof of stability of N-front solutions of the FitzHugh-Nagumo equations

Consideration is devoted to traveling N-front wave solutions of the FitzHugh-Nagumo equations of the bistable type. Especially, stability of the N-front wave is proven. In the proof, the eigenvalue problem for the N-front wave bifurcating from coexisting simple front and back waves is regarded as a bifurcation problem for projectivised eigenvalue equations, and a topological index is employed to detect eigenvalues.