, Volume 109, Issue 1, pp 75-86
Date: 10 Feb 2009

Integrability of Kupershmidt Deformations

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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).

This work was supported in part by NWO-RFBR grant 047017015 (PK, IK, and AV), RFBR-E.I.N.S.T.E.IN Consortium grant 06-01-92060 (IK, AV, and RV), and RFBR-CRNS grant 08-07-92496 (IK and AV).