Integrability of Dirac reduced bi-Hamiltonian equations
  First, we give a brief review of the theory of the Lenard-Magri scheme for a non-local bi-Poisson structure and of the theory of Dirac reduction. These theories are used in the remainder of the paper to prove integrability of three hierarchies of bi-Hamiltonian PDE's, obtained by Dirac reduction from some generalized Drinfeld-Sokolov hierarchies. 
Alberto De Sole, Victor G. Kac, Daniele Valeri
math-ph math.MP math.RA math.RT nlin.SI