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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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2020 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2020
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/210690 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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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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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Multi-Component Extension of CAC Systems Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Multi-Component Extension of CAC Systems |
| spellingShingle |
Multi-Component Extension of CAC Systems Zhang, Dan-Da van der Kamp, Peter H. Zhang, Da-Jun |
| title_short |
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_sort |
multi-component extension of cac systems |
| 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 |
| publishDate |
2020 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| 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.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/210690 |
| 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 |
| work_keys_str_mv |
AT zhangdanda multicomponentextensionofcacsystems AT vanderkamppeterh multicomponentextensionofcacsystems AT zhangdajun multicomponentextensionofcacsystems |
| first_indexed |
2025-12-17T12:04:30Z |
| last_indexed |
2025-12-17T12:04:30Z |
| _version_ |
1851756978085298176 |