Theoretical and Mathematical Physics

, Volume 171, Issue 1, pp 442–447 | Cite as

Bi-Hamiltonian ordinary differential equations with matrix variables



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.


integrable ordinary differential equation with matrix unknowns bi-Hamiltonian formalism Manakov model 


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Copyright information

© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  • A. V. Odesskii
    • 1
  • V. N. Rubtsov
    • 2
    • 3
  • V. V. Sokolov
    • 4
  1. 1.Brock UniversitySt. CatharinesCanada
  2. 2.Institute for Theoretical and Experimental PhysicsMoscowRussia
  3. 3.LAREMA, CNRSUniversité d’AngersAngersFrance
  4. 4.Landau Institute for Theoretical PhysicsRASMoscowRussia

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