Flat bidifferential ideals and semihamiltonian PDEs
  In this paper we consider a class of semihamiltonian systems characterized by the existence of a special conservation law.   The density and the current of this conservation law satisfy a second order system of PDEs which has a natural interpretation in the theory of flat bifferential ideals. The class of systems we consider contains important well-known examples of semihamiltonian systems. Other examples, like genus 1   Whitham modulation equations for KdV, are related to this class by a reciprocal trasformation. 
Paolo Lorenzoni