Bi-Hamiltonian ODEs with matrix variables

Alexander Odesskii; Vladimir Rubtsov; Vladimir Sokolov

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Bi-Hamiltonian ODEs with matrix variables

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arxiv 1105.1740 v1 pith:JBB5RSRI submitted 2011-05-09 nlin.SI

Alexander Odesskii , Vladimir Rubtsov , Vladimir Sokolov This is my paper · ORCID

classification nlin.SI

keywords bracketsmatrixlinearquadraticvariablesarbitrarybi-hamiltoniancase

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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.

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