Mathematical Notes

, Volume 64, Issue 1, pp 98–109 | Cite as

Canonically conjugate variables for the Volterra lattice with periodic boundary conditions

  • A. V. Penskoi


The Volterra lattice is considered. This dynamical system is known to be Hamiltonian with respect to two compatible Poisson brackets (quadratic and cubic). For each of the two brackets, a set of canonically conjugate variables is found by using the spectral theory of the Jacobi operator.

Key words

integrable system Volterra model periodic boundary conditions Toda lattice Poisson bracket canonically conjugate variables Jacobi operator 


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Copyright information

© Plenum Publishing Corporation 1999

Authors and Affiliations

  • A. V. Penskoi
    • 1
  1. 1.M. V. Lomonosov Moscow State UniversityUSSR

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