Existence of traveling waves and applications

In this thesis, we consider a partial differential equation which is related to a one dimensional array of Chua's circuits. We show existence of traveling waves for that equation by considering the existence of heteroclinic orbits of an ordinary differential equation. Our main contribution is an analytical approach. This is based on the classical singular perturbation theory of matched asymptotics and the center manifold theory. We are also able to obtain some generalization for boundary value problems with infinite time intervals. The results are useful in some other applications.