Integrability of Dirac reduced bi-Hamiltonian equations
arXiv:1401.6006 · doi:10.1007/978-3-319-05254-0_2
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's, obtained by Dirac reduction from some generalized Drinfeld-Sokolov hierarchies.
15 pages. Corrected some typos and added missing equations in Section 5 for g=sl_n, n>2