Integrability of Kupershmidt deformations

P.H.M. Kersten, I.S. Krasil'shchik, A.M. Verbovetsky, R. Vitolo

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    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).
    Original languageEnglish
    Pages (from-to)75-86
    JournalActa applicandae mathematicae
    Issue number1
    Publication statusPublished - 2010


    • Nonlinear differential equations
    • Variational Schouten bracket
    • Hamiltonian structures
    • Symmetries
    • Conservation laws

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