Mikhailov, A.V orcid.org/0000-0003-4238-6995, Novikov, V.S and Wang, J.P (Cover date: July 2022) Perturbative Symmetry Approach for Differential–Difference Equations. Communications in Mathematical Physics, 393. 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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The Author(s) 2022. This is an open access article under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits unrestricted use, distribution and reproduction in any medium, provided the original work is properly cited. |
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: | 01 Apr 2022 14:31 |
Last Modified: | 28 Sep 2023 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:185342 |