Integrability of Kupershmidt Deformations
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- 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
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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).