Exterior Differential Systems and Hyperbolic PDE

Many problems in geometry and physics can naturally be expressed in terms of the vanishing of a collection differential forms on a manifold. Such an equation involving differential forms is called an exterior differential system (EDS). In particular, a class of hyperbolic PDE can be so expressed and the geometric structure of the corresponding EDS can be used to study the solutions of the PDE. In this project you will use this theory to explore the Konno-Oono coupled integrable dispersionless PDE system that plays a role a number of fields in physics. Time permitting, its relation to surfaces of constant negative curvature and to the inverse scattering transform may also be studied.