Bi-Hamiltonian ODEs with matrix variables
  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. 
Alexander Odesskii, Vladimir Rubtsov and Vladimir Sokolov
nlin.SI