Integrability of Kupershmidt Deformations

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

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    13 Citations (Scopus)

    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).
    Original languageUndefined
    Pages (from-to)75-86
    JournalActa applicandae mathematicae
    Volume109
    Issue number1
    DOIs
    Publication statusPublished - 2010

    Keywords

    • Nonlinear differential equations - Variational Schouten bracket - Hamiltonian structures - Symmetries - Conservation laws
    • IR-69569

    Cite this

    Kersten, P. H. M., Krasil'shchik, I., Verbovetsky, A. M., & Vitolo, R. (2010). Integrability of Kupershmidt Deformations. Acta applicandae mathematicae, 109(1), 75-86. https://doi.org/10.1007/s10440-009-9442-4