Geodesic
Bi-Hamiltonian ordinary differential equations with matrix variables
Teoretičeskaâ i matematičeskaâ fizika, Tome 171 (2012) no. 1, pp. 26-32
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We consider a special class of Poisson brackets related to systems of ordinary differential equations with matrix variables. We investigate general properties of such brackets, present an example of a compatible pair of quadratic and linear brackets, and find the corresponding hierarchy of integrable models, which generalizes the two-component Manakov matrix system to the case of an arbitrary number of matrices.
Keywords: integrable ordinary differential equation with matrix unknowns, bi-Hamiltonian formalism, Manakov model. 
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A. V. Odesskii; V. N. Rubtsov; V. V. Sokolov. Bi-Hamiltonian ordinary differential equations with matrix variables. Teoretičeskaâ i matematičeskaâ fizika, Tome 171 (2012) no. 1, pp. 26-32. http://geodesic.mathdoc.fr/item/TMF_2012_171_1_a2/

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