De Sole, A., Kac, V. G., Valeri, D. and Wakimoto, M. (2020) Poisson λ-brackets for differential-difference equations. International Mathematics Research Notices, 2020(13), pp. 4144-4190. (doi: 10.1093/imrn/rny242)
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Abstract
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.
| Item Type: | Articles |
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| Additional Information: | This work was supported in part by the Department of Mathematics, Massachusetts Institute of Technology [to M.W.]. |
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Valeri, Dr Daniele |
| Authors: | De Sole, A., Kac, V. G., Valeri, D., and Wakimoto, M. |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
| Journal Name: | International Mathematics Research Notices |
| Publisher: | Oxford University Press |
| ISSN: | 1073-7928 |
| ISSN (Online): | 1687-0247 |
| Published Online: | 30 October 2018 |
| Copyright Holders: | Copyright © 2018 The Authors |
| First Published: | First published in International Mathematics Research Notices 2020(13): 4144-4190 |
| Publisher Policy: | Reproduced in accordance with the copyright policy of the publisher |
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