BIHAMILTONIAN GEOMETRY, DARBOUX COVERINGS, AND LINEARIZATION OF THE KP HIERARCHY

We use ideas of the geometry of bihamiltonian manifolds, developed by Gel'fand and Zakharevich, to study the KP equations. In this approach they have the form of local conservation laws, and can be traded for a system of ordinary differential equations of Riccati type, which we c all the Central System. We show that the latter can be linearized by m eans of a Darboux covering, and we use this procedure as an alternativ e technique to construct rational solutions of the KP equations.