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Poisson λ-brackets for Differential–Difference Equations

Author(s)
De Sole, Alberto; Kac, Victor G; Valeri, Daniele; Wakimoto, Minoru
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Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/
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Abstract
© 2018 The Author(s). Published by Oxford University Press. All rights reserved. We introduce the notion of a multiplicative Poisson λ-bracket, which plays the same role in the theory of Hamiltonian differential-difference equations as the usual Poisson λ-bracket plays in the theory of Hamiltonian partial differential equations (PDE). We classify multiplicative Poisson λ-brackets in one difference variable up to order 5. As an example, we demonstrate how to apply the Lenard-Magri scheme to a compatible pair of multiplicative Poisson λ-brackets of order 1 and 2, to establish integrability of the Volterra chain.
Date issued
2018
URI
https://hdl.handle.net/1721.1/136216
Journal
International Mathematics Research Notices
Publisher
Oxford University Press (OUP)

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