Local Wellposedness of quasilinear systems of PDE generalizing KdV

In this talk I will discuss local well-posedness of an Initial Value problem associated to a system of PDE's generalizing the Korteweg-de Vries Equation (KdV). These results, inspired by the approach of  Kenig-Ponce-Vega from the Quasi-Linear Schrödinger equation, apply to a large class of systems of KdV type. I will discuss several approaches to the KdV-type problems emphasizing the energy method and local smoothing estimates that are essential to my proof.