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).

Integrability of Kupershmidt deformations

VITOLO, Raffaele
2010-01-01

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).
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11587/327719
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