Caudrelier, V orcid.org/0000-0003-0129-6758, van der Kamp, PH and Zhang, C (2022) Integrable boundary conditions for quad equations, open boundary reductions and integrable mappings. International Mathematics Research Notices, 2022 (22). pp. 18110-18153. ISSN 1073-7928
Abstract
In the context of integrable difference equations on quad-graphs, we introduce the method of open boundary reductions, as an alternative to the well-known periodic reductions, for constructing discrete integrable mappings and their invariants. The mappings are obtained from well-posed initial value problems for quad and boundary equations restricted to strips on Z2-lattices. The invariants are constructed using Sklyanin’s double-row monodromy matrix. To establish its properties, we use the discrete zero curvature condition and boundary zero curvature condition, showing how the latter derives from the boundary consistency condition. We focus on the Adler–Bobenko–Suris classification and associated integrable boundary equations. Examples are given for the H1 and Q1(δ=0) equations, leading to novel maps of the plane.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The Author(s) 2021. Published by Oxford University Press. All rights reserved. This is an author produced version of an article published in International Mathematics Research Notices. Uploaded in accordance with the publisher's self-archiving policy. |
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: | 12 Aug 2021 14:16 |
Last Modified: | 10 Aug 2023 13:34 |
Status: | Published |
Publisher: | Oxford University Press |
Identification Number: | 10.1093/imrn/rnab188 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:176902 |