A Study of Dispersive Evolution Equations with Nonlocal Nonlinearities

In this thesis we consider a nonlinear-nonlocal equation of Whitham type. We prove the local well-posedness for our equation in the fractional Sobolev space by using the Picard Lindelöf existence theorem to prove the existence of a unique solution. Additionally, we use the Crandall-Rabinowitz local bifurcation theorem to prove the existence of periodic traveling waves to our nonlinear-nonlocal equation