Acta Applicandae Mathematicae

, Volume 109, Issue 1, pp 75–86

Integrability of Kupershmidt Deformations

  • P. H. M. Kersten
  • I. S. Krasil’shchik
  • A. M. Verbovetsky
  • R. Vitolo
Article

DOI: 10.1007/s10440-009-9442-4

Cite this article as:
Kersten, P.H.M., Krasil’shchik, I.S., Verbovetsky, A.M. et al. Acta Appl Math (2010) 109: 75. doi:10.1007/s10440-009-9442-4

Abstract

We prove that the Kupershmidt deformation of a bi-Hamiltonian system is itself bi-Hamiltonian. Moreover, Magri hierarchies of the initial system give rise to Magri hierarchies of Kupershmidt deformations as well. Since Kupershmidt deformations are not written in evolution form, we start with an outline a geometric framework to study Hamiltonian properties of general non-evolution differential equations, developed in Igonin et al. (to appear, 2009) (see also Kersten et al., In: Differential Equations: Geometry, Symmetries and Integrability, Springer, Berlin, 2009).

Keywords

Nonlinear differential equations Variational Schouten bracket Hamiltonian structures Symmetries Conservation laws 

Mathematics Subject Classification (2000)

37K05 35Q53 

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

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

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