Integrability of Dirac reduced bi-Hamiltonian equations
Mathematical Physics
2015-12-18 v2 math.MP
Rings and Algebras
Representation Theory
Exactly Solvable and Integrable Systems
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.
Keywords
Cite
@article{arxiv.1401.6006,
title = {Integrability of Dirac reduced bi-Hamiltonian equations},
author = {Alberto De Sole and Victor G. Kac and Daniele Valeri},
journal= {arXiv preprint arXiv:1401.6006},
year = {2015}
}
Comments
15 pages. Corrected some typos and added missing equations in Section 5 for g=sl_n, n>2