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Hamiltonian Structures for General PDEs

  • P. KerstenEmail author
  • I. S. Krasil′shchik
  • A. M. Verbovetsky
  • R. Vitolo
Chapter
Part of the Abel Symposia book series (ABEL, volume 5)

Abstract

We sketch out a new geometric framework to construct Hamiltonian operators for generic, non-evolutionary partial differential equations. Examples on how the formalism works are provided for the KdV equation, Camassa-Holm equation, and Kupershmidt’s deformation of a bi-Hamiltonian system.

Keywords

Hamiltonian differential equation bi-Hamiltonian system non-evolution equation Camassa-Holm equation Kupershmidt’s deformation 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • P. Kersten
    • 2
    Email author
  • I. S. Krasil′shchik
    • 1
  • A. M. Verbovetsky
    • 1
  • R. Vitolo
    • 3
  1. 1.Independent University of MoscowMoscowRussia
  2. 2.University of TwenteEnschedeThe Netherlands
  3. 3.Department of Mathematics “E. De Giorgi”Università del SalentoLecceItaly

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