Theoretical and Mathematical Physics

, Volume 149, Issue 2, pp 1425–1436 | Cite as

Pairs of commuting Hamiltonians quadratic in the momenta

  • V. G. Marikhin
  • V. V. Sokolov
Article

Abstract

In the case of two degrees of freedom, we consider pairs of Hamiltonians quadratic in the momenta and commuting with respect to the standard Poisson bracket. We find new multiparameter families of such pairs and present a universal scheme for constructing a complete solution of the Hamilton-Jacobi equation in terms of integrals over an algebraic curve. For the most complicated examples, this curve is a nonhyperelliptic covering of an elliptic curve.

Keywords

integrable Hamiltonian system separation of variables algebraic system 

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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • V. G. Marikhin
    • 1
  • V. V. Sokolov
    • 1
  1. 1.Landau Institute of Theoretical PhysicsRASMoscowRussia

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