Integrability of Kupershmidt deformations

Details Integrability of Kupershmidt deformations Integrability of Kupershmidt deformations

2008-12-29

arxiv.org/abs/0812.4902v2

Acta Appl. Math. 109 (2010), 75-86

Nonlinear Sciences

Exactly Solvable and Integrable Systems

11 pages; v2: minor corrections

Scientific paper

10.1007/s10440-009-9442-4

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).

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