Fordy, AP orcid.org/0000-0002-2523-0262 and Xenitidis, P (2017) ZN graded discrete Lax pairs and Yang-Baxter maps. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 473 (2201). 20160946. ISSN 1364-5021
Abstract
We recently introduced a class of ZN graded discrete Lax pairs and studied the associated discrete integrable systems (lattice equations). In this paper, we introduce the corresponding Yang–Baxter maps. Many well-known examples belong to this scheme for N=2, so, for N≥3, our systems may be regarded as generalizations of these. In particular, for each N we introduce a class of multi-component Yang–Baxter maps, which include HBIII (of Papageorgiou et al. 2010 SIGMA 6, 003 (9 p). (doi:10.3842/SIGMA.2010.033)), when N=2, and that associated with the discrete modified Boussinesq equation, for N=3. For N≥5 we introduce a new family of Yang–Baxter maps, which have no lower dimensional analogue. We also present new multi-component versions of the Yang–Baxter maps FIV and FV (given in the classification of Adler et al. 2004 Commun. Anal. Geom. 12, 967–1007. (doi:10.4310/CAG.2004.v12.n5.a1).
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | (c) 2017 The Author(s). Published by the Royal Society. All rights reserved. This is an author produced version of a paper published in Proceedings of the Royal Society A. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | discrete integrable system, Lax pair, symmetry, Yang–Baxter map |
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: | 25 Jul 2017 14:20 |
Last Modified: | 01 May 2018 00:38 |
Status: | Published |
Publisher: | Royal Society |
Identification Number: | 10.1098/rspa.2016.0946 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:119445 |