Mikhailov, A.V. orcid.org/0000-0003-4238-6995, Novikov, V.S. and Wang, J.P. (2022) Perturbative Symmetry Approach for Differential-Difference Equations. Communications in Mathematical Physics, 393 (2). pp. 1063-1104. ISSN 0010-3616
Abstract
We propose a new method to tackle the integrability problem for evolutionary differential–difference equations of arbitrary order. It enables us to produce necessary integrability conditions, to determine whether a given equation is integrable or not, and to advance in classification of integrable equations. We define and develop symbolic representation for the difference polynomial ring, difference operators and formal series. In order to formulate necessary integrability conditions, we introduce a novel quasi-local extension of the difference ring. We apply the developed formalism to solve the classification problem of integrable equations for anti-symmetric quasi-linear equations of order (- 3 , 3) and produce a list of 17 equations satisfying the necessary integrability conditions. For every equation from the list we present an infinite family of integrable higher order relatives. Some of the equations obtained are new.
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Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The Author(s) 2022. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
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: | 20 Dec 2024 11:32 |
Last Modified: | 20 Dec 2024 11:32 |
Status: | Published |
Publisher: | Springer |
Identification Number: | 10.1007/s00220-022-04383-0 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:221025 |
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