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Teoreticheskaya i Matematicheskaya Fizika, 2025, Volume 224, Number 1, Pages 63–77
DOI: https://doi.org/10.4213/tmf10982 (Mi tmf10982) 		 
This article is cited in 1 scientific paper (total in 1 paper)

From NLS-type matrix refactorization problems to set-theoretic solutions of the 2- and 3-simplex equations

S. Konstantinou-Rizos

Center of Integrable Systems, Demidov Yaroslavl State University, Yaroslavl, Russia
Full-text PDF (444 kB) First page Citations (1) English version article
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DOI: https://doi.org/10.4213/tmf10982
Abstract: We present a method for constructing hierarchies of solutions of $n$-simplex equations by varying the spectral parameter in their Lax representation. We use this method to derive new solutions of the set-theoretic $2$- and $3$-simplex equations that are related to the Adler map and nonlinear Schrödinger (NLS) type equations. Moreover, we prove that some of the derived Yang–Baxter maps are completely integrable.
Keywords: Yang–Baxter maps, Zamolodchikov tetrahedron equation, NLS equation, Adler map, NLS-type Yang–Baxter maps, variation of the spectral parameter.
Funding agency Grant number
Russian Science Foundation 20-71-10110
Ministry of Science and Higher Education of the Russian Federation 075-02-2025-1636
The work on Secs. 2, 3 and 4 was funded by the Russian Science Foundation under grant No. 20-71-10110, https://rscf.ru/en/project/23-71-50012/. The work on Secs. 1, 5, and 6 was supported by the Ministry of Science and Higher Education of the Russian Federation (agreement No. 075-02-2025-1636).
Received: 16.03.2025
Revised: 23.03.2025
Published: 13.08.2025
English version:
Theoretical and Mathematical Physics, 2025, Volume 224, Issue 1, Pages 1154–1166
DOI: https://doi.org/10.1134/S0040577925070050
Bibliographic databases:
Document Type: Article
PACS: 02.30.Ik, 02.90.+p, 03.65.Fd
MSC: 35Q55, 16T25
Language: Russian
Citation: S. Konstantinou-Rizos, “From NLS-type matrix refactorization problems to set-theoretic solutions of the 2- and 3-simplex equations”, TMF, 224:1 (2025), 63–77; Theoret. and Math. Phys., 224:1 (2025), 1154–1166
Citation in format AMSBIB
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\by S.~Konstantinou-Rizos
\paper From NLS-type matrix refactorization problems to set-theoretic solutions of the~2- and 3-simplex equations
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\pages 63--77
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\jour Theoret. and Math. Phys.
\yr 2025
\vol 224
\issue 1
\pages 1154--1166
\crossref{https://doi.org/10.1134/S0040577925070050}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-105011737094}
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    • This publication is cited in the following 1 articles:
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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