Bi-Hamiltonian ODEs with matrix variables

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.
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https://hal.archives-ouvertes.fr/hal-00619676
Contributor : Vladimir Roubtsov <>
Submitted on : Tuesday, September 6, 2011 - 5:09:14 PM
Last modification on : Wednesday, December 19, 2018 - 2:08:04 PM

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  • HAL Id : hal-00619676, version 1
  • ARXIV : 1105.1740

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Alexander Odesskii, Vladimir Rubtsov, Vladimir Sokolov. Bi-Hamiltonian ODEs with matrix variables. 2011. ⟨hal-00619676⟩

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