Bi-Hamiltonian ordinary differential equations with matrix variables
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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.
Keywordsintegrable ordinary differential equation with matrix unknowns bi-Hamiltonian formalism Manakov model
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