  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.
