Fordy, AP orcid.org/0000-0002-2523-0262 and Xenitidis, P (2017) ΖN graded discrete Lax pairs and integrable difference equations. Journal of Physics A: Mathematical and Theoretical, 50 (16). 165205. ISSN 1751-8113
Abstract
We introduce a class of ZN graded discrete Lax pairs, with NxN matrices, linear in the spectral parameter. We give a classification scheme for such Lax pairs and the associated integrable lattice systems. We present two potential forms and completely classify the generic case. Many well known examples belong to our scheme for N = 2, so many of our systems may be regarded as generalisations of these. Even at N = 3, several new integrable systems arise. A decomposable case gives rise to interesting coupled systems of lower dimensional equations. Many of our equations are mutually compatible, so can be used together to form 'coloured' lattices.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2017 IOP Publishing Ltd. This is an author-created, un-copyedited version of an article published in Journal of Physics A: Mathematical and Theoretical. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://doi.org/10.1088/1751-8121/aa639a |
Keywords: | discrete integrable system, lattice equations, Lax pair, backlund transformation, 3D consistency |
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: | 04 Apr 2017 11:19 |
Last Modified: | 09 Sep 2020 16:17 |
Status: | Published |
Publisher: | IOP Publishing |
Identification Number: | 10.1088/1751-8121/aa639a |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:114494 |