Multi-Component Extension of CAC Systems

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dc.contributor.authorZhang, Dan-Da
dc.contributor.authorvan der Kamp, Peter H.
dc.contributor.authorZhang, Da-Jun
dc.date.accessioned2025-12-15T15:15:35Z
dc.date.issued2020
dc.description.abstractIn 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.
dc.description.sponsorshipThe 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.
dc.identifier.citationMulti-Component Extension of CAC Systems. Dan-Da Zhang, Peter H. van der Kamp and Da-Jun Zhang. SIGMA 16 (2020), 060, 30 pages
dc.identifier.doihttps://doi.org/10.3842/SIGMA.2020.060
dc.identifier.issn1815-0659
dc.identifier.other2020 Mathematics Subject Classification: 37K60
dc.identifier.otherarXiv:1912.00713
dc.identifier.urihttps://nasplib.isofts.kiev.ua/handle/123456789/210690
dc.language.isoen
dc.publisherІнститут математики НАН України
dc.relation.ispartofSymmetry, Integrability and Geometry: Methods and Applications
dc.statuspublished earlier
dc.titleMulti-Component Extension of CAC Systems
dc.typeArticle

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Symmetry, Integrability and Geometry: Methods and Applications, 2020, том 16, випуск за цей рік