Integrability of Kupershmidt deformations
  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 [2] (see also arXiv:0812.4895). 
Paul Kersten, Iosif Krasil'shchik, Alexander Verbovetsky, and Raffaele   Vitolo