Integrability of Kupershmidt deformations

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 [2] (see also arXiv:0812.4895).

11 pages; v2: minor corrections

References in corpus (3)

• KdV6: An Integrable System
• A new integrable generalization of the Korteweg - de Vries equation
• Hamiltonian structures for general PDEs

Cited by in corpus (8)

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• Hamiltonian structures for general PDEs
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• On Negative Order KdV Equations
• Some new integrable systems constructed from the bi-Hamiltonian systems with pure differential Hamiltonian operators