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Bihamiltonian Systems and Lax Representation

  • J. J. Morales
  • R. Ramirez
Part of the NATO ASI Series book series (NSSB, volume 331)

Abstract

Between the methods for obtaining first integrals of hamiltonian systems there are two that have acquired more and more relevance in the study of integrable hamiltonian systems, they are the following:
  1. (1).
    The representation of the system as a Lax Pair
    $$\dot L = \left[ {L,\,A} \right],$$
    , where L, A belong to a Lie algebra.
     
  2. (2).

    The bihamiltonian method, which consist in the existence of an alternative Poisson bracket, such that the linear combinations of this bracket with the original one are a Poisson bracket too and the hamiltonian equation of the second bracket, with respect to some hamiltonian, is the same that the original one.

     

Keywords

Hamiltonian System Poisson Bracket Toda Lattice Integrable Hamiltonian System Casimir Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • J. J. Morales
    • 1
  • R. Ramirez
    • 1
  1. 1.Departament de Matemàtica Aplicada IIBarcelonaSpain

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