Integrability of Kupershmidt Deformations


Kersten, P.H.M. and Krasil'shchik, I.S. and Verbovetsky, A.M. and Vitolo, R. (2010) Integrability of Kupershmidt Deformations. Acta Applicandae Mathematicae, 109 (1). pp. 75-86. ISSN 0167-8019

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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).
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Copyright:© 2010 Springer
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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