Xu, X, Jiang, M and Nijhoff, FW (2021) Integrable symplectic maps associated with discrete Korteweg-de Vries-type equations. Studies in Applied Mathematics, 146 (1). pp. 233-278. ISSN 0022-2526
Abstract
In this paper, we present novel integrable symplectic maps, associated with ordinary difference equations, and show how they determine, in a remarkably diverse manner, the integrability, including Lax pairs and the explicit solutions, for integrable partial difference equations which are the discrete counterparts of integrable partial differential equations of Korteweg‐de Vries‐type (KdV‐type). As a consequence it is demonstrated that several distinct Hamiltonian systems lead to one and the same difference equation by means of the Liouville integrability framework. Thus, these integrable symplectic maps may provide an efficient tool for characterizing, and determining the integrability of, partial difference equations.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2020 Wiley Periodicals LLC. This is the peer reviewed version of the following article: Xu, X, Jiang, M and Nijhoff, FW (2021) Integrable symplectic maps associated with discrete Korteweg-de Vries-type equations. Studies in Applied Mathematics, 146 (1). pp. 233-278. ISSN 0022-2526, which has been published in final form at Studies in Applied Mathematics. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions. |
Keywords: | Baker‐Akhiezer functions; discrete Korteweg‐de Vries‐type equations; finite genus solutions; integrable Hamiltonian systems; integrable symplectic maps |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 29 Sep 2020 09:42 |
Last Modified: | 19 Jul 2022 09:02 |
Status: | Published |
Publisher: | Wiley |
Identification Number: | 10.1111/sapm.12346 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:165848 |