The Soliton Equations associated with the Affine Kac-Moody Lie Algebra   G_2^{(1)}
  We construct in an explict way the soliton equation corresponding to the affine Kac--Moody Lie algebra $G_2^{(1)}$ together with their bihamiltonian structure. Moreover the Riccati equation satisfied by the generating function of the commuting Hamiltonians densities is also deduced. Finally we describe a way to deduce the bihamiltonian equations directly in terms of this latter functions 
Paolo Casati, Alberto Della Vedova, Giovanni Ortenzi