Bi-Hamiltonian ODEs with matrix variables

Authors :: Odesskii, Alexander
Rubtsov, Vladimir
Sokolov, Vladimir
Laboratoire Angevin de Recherche en Mathématiques (LAREMA)
Université d'Angers (UA)-Centre National de la Recherche Scientifique (CNRS)
ANR DIADEMS
PICS
Roubtsov, Vladimir
Publication Year :: 2011
Publisher :: HAL CCSD, 2011.
Abstract: We consider a special class of linear and quadratic Poisson brackets related to ODE systems with matrix variables. We investigate general properties of such brackets, present an example of a compatible pair of quadratic and linear brackets and found the corresponding hierarchy of integrable models, which generalizes the two-component Manakov's matrix system in the case of arbitrary number of matrices.<br />Comment: 9 pages, latex