@article {2014, title = {Integrability of Dirac reduced bi-Hamiltonian equations}, number = {arXiv:1401.6006;}, year = {2014}, note = {15 pages}, institution = {SISSA}, abstract = {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{\textquoteright}s, obtained by Dirac reduction from some generalized Drinfeld-Sokolov hierarchies.}, url = {http://hdl.handle.net/1963/7247}, author = {Alberto De Sole and Victor G. Kac and Daniele Valeri} }