THE EXISTENCE OF INFINITELY MANY TRAVELING FRONT AND BACK WAVES IN THE FITZHUGH-NAGUMO EQUATIONS

Consideration is given to the FitzHugh-Nagumo equations of bistable type. The existence of traveling front and back waves with any finite number of pulses is proved. The speed of such a multiple pulse wave is characterized by its number of pulses: the more pulses it has, the slower it travels. Traveling impulse and traveling train solutions are also found. These traveling waves arise from the bifurcation of a doubly twisted front-back wave loop. The method is based on the theory of heteroclinic loop bifurcation, the geometric theory of singular perturbation and the Melnikov method.