Multi-Component Extension of CAC Systems

In this paper, an approach to generate multidimensionally consistent N-Component systems is proposed. The approach starts from scalar multidimensionally consistent quadrilateral systems and makes use of the cyclic group. The obtained N-component systems inherit integrable features such as Bäcklund t...

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Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2020
Hauptverfasser: Zhang, Dan-Da, van der Kamp, Peter H., Zhang, Da-Jun
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут математики НАН України 2020
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/210690
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren:Multi-Component Extension of CAC Systems. Dan-Da Zhang, Peter H. van der Kamp and Da-Jun Zhang. SIGMA 16 (2020), 060, 30 pages

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Zhang, Dan-Da
van der Kamp, Peter H.
Zhang, Da-Jun
author_facet Zhang, Dan-Da
van der Kamp, Peter H.
Zhang, Da-Jun
citation_txt Multi-Component Extension of CAC Systems. Dan-Da Zhang, Peter H. van der Kamp and Da-Jun Zhang. SIGMA 16 (2020), 060, 30 pages
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description In this paper, an approach to generate multidimensionally consistent N-Component systems is proposed. The approach starts from scalar multidimensionally consistent quadrilateral systems and makes use of the cyclic group. The obtained N-component systems inherit integrable features such as Bäcklund transformations and Lax pairs, and exhibit interesting aspects, such as nonlocal reductions. Higher-order single-component lattice equations (on larger stencils) and multi-component discrete Painlevé equations can also be derived in the context, and the approach extends to N-component generalizations of higher-dimensional lattice equations.
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format Article
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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1815-0659
language English
last_indexed 2025-12-17T12:04:30Z
publishDate 2020
publisher Інститут математики НАН України
record_format dspace
spelling Zhang, Dan-Da
van der Kamp, Peter H.
Zhang, Da-Jun
2025-12-15T15:15:35Z
2020
Multi-Component Extension of CAC Systems. Dan-Da Zhang, Peter H. van der Kamp and Da-Jun Zhang. SIGMA 16 (2020), 060, 30 pages
1815-0659
2020 Mathematics Subject Classification: 37K60
arXiv:1912.00713
https://nasplib.isofts.kiev.ua/handle/123456789/210690
https://doi.org/10.3842/SIGMA.2020.060
In this paper, an approach to generate multidimensionally consistent N-Component systems is proposed. The approach starts from scalar multidimensionally consistent quadrilateral systems and makes use of the cyclic group. The obtained N-component systems inherit integrable features such as Bäcklund transformations and Lax pairs, and exhibit interesting aspects, such as nonlocal reductions. Higher-order single-component lattice equations (on larger stencils) and multi-component discrete Painlevé equations can also be derived in the context, and the approach extends to N-component generalizations of higher-dimensional lattice equations.
The authors thank Jarmo Hietarinta for his suggestion to include equations (2.20) and (2.21), noting they are not of the same form. We thank Pavlos Kassotakis and Maciej Nieszporski for noting that equation (3.13) can be written as a quadrilateral system. We thank all referees for their comments, especially the referee who pointed out Appendix B from [8]. DJZ is grateful to Professors Q.P. Liu and R.G. Zhou for their warm discussion. This project is supported by the NSF of China (grant nos. 11875040, 11631007, and 11801289), the K.C. Wong Magna Fund in Ningbo University, and a CRSC grant from La Trobe University.
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Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Multi-Component Extension of CAC Systems
Article
published earlier
spellingShingle Multi-Component Extension of CAC Systems
Zhang, Dan-Da
van der Kamp, Peter H.
Zhang, Da-Jun
title Multi-Component Extension of CAC Systems
title_full Multi-Component Extension of CAC Systems
title_fullStr Multi-Component Extension of CAC Systems
title_full_unstemmed Multi-Component Extension of CAC Systems
title_short Multi-Component Extension of CAC Systems
title_sort multi-component extension of cac systems
url https://nasplib.isofts.kiev.ua/handle/123456789/210690
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