The Elliptic Painlevé Lax Equation vs. van Diejen's 8-Coupling Elliptic Hamiltonian
The 8-parameter elliptic Sakai difference Painlevé equation admits a Lax formulation. We show that a suitable specialization of the Lax equation gives rise to the time-independent Schrödinger equation for the BC₁ 8-parameter 'relativistic' Calogero-Moser Hamiltonian due to van Diejen. This...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2020 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2020
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/210785 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | The Elliptic Painlevé Lax Equation vs. van Diejen's 8-Coupling Elliptic Hamiltonian. Masatoshi Noumi, Simon Ruijsenaars and Yasuhiko Yamada. SIGMA 16 (2020), 063, 16 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862667515013890048 |
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| author | Noumi, Masatoshi Ruijsenaars, Simon Yamada, Yasuhiko |
| author_facet | Noumi, Masatoshi Ruijsenaars, Simon Yamada, Yasuhiko |
| citation_txt | The Elliptic Painlevé Lax Equation vs. van Diejen's 8-Coupling Elliptic Hamiltonian. Masatoshi Noumi, Simon Ruijsenaars and Yasuhiko Yamada. SIGMA 16 (2020), 063, 16 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | The 8-parameter elliptic Sakai difference Painlevé equation admits a Lax formulation. We show that a suitable specialization of the Lax equation gives rise to the time-independent Schrödinger equation for the BC₁ 8-parameter 'relativistic' Calogero-Moser Hamiltonian due to van Diejen. This amounts to a generalization of previous results concerning the Painlevé-Calogero correspondence to the highest level in the two hierarchies.
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| first_indexed | 2026-03-16T11:08:37Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-210785 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-16T11:08:37Z |
| publishDate | 2020 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Noumi, Masatoshi Ruijsenaars, Simon Yamada, Yasuhiko 2025-12-17T14:38:54Z 2020 The Elliptic Painlevé Lax Equation vs. van Diejen's 8-Coupling Elliptic Hamiltonian. Masatoshi Noumi, Simon Ruijsenaars and Yasuhiko Yamada. SIGMA 16 (2020), 063, 16 pages 1815-0659 2020 Mathematics Subject Classification: 39A06; 33E05 arXiv:1903.09738 https://nasplib.isofts.kiev.ua/handle/123456789/210785 https://doi.org/10.3842/SIGMA.2020.063 The 8-parameter elliptic Sakai difference Painlevé equation admits a Lax formulation. We show that a suitable specialization of the Lax equation gives rise to the time-independent Schrödinger equation for the BC₁ 8-parameter 'relativistic' Calogero-Moser Hamiltonian due to van Diejen. This amounts to a generalization of previous results concerning the Painlevé-Calogero correspondence to the highest level in the two hierarchies. The research reported in this article was initiated during a visit of S.R. to the Department of Mathematics of Kobe University. He would like to thank the Department for its hospitality and financial support. This work is supported by JSPS KAKENHI Grant Numbers 26287018 and 15H03626. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications The Elliptic Painlevé Lax Equation vs. van Diejen's 8-Coupling Elliptic Hamiltonian Article published earlier |
| spellingShingle | The Elliptic Painlevé Lax Equation vs. van Diejen's 8-Coupling Elliptic Hamiltonian Noumi, Masatoshi Ruijsenaars, Simon Yamada, Yasuhiko |
| title | The Elliptic Painlevé Lax Equation vs. van Diejen's 8-Coupling Elliptic Hamiltonian |
| title_full | The Elliptic Painlevé Lax Equation vs. van Diejen's 8-Coupling Elliptic Hamiltonian |
| title_fullStr | The Elliptic Painlevé Lax Equation vs. van Diejen's 8-Coupling Elliptic Hamiltonian |
| title_full_unstemmed | The Elliptic Painlevé Lax Equation vs. van Diejen's 8-Coupling Elliptic Hamiltonian |
| title_short | The Elliptic Painlevé Lax Equation vs. van Diejen's 8-Coupling Elliptic Hamiltonian |
| title_sort | elliptic painlevé lax equation vs. van diejen's 8-coupling elliptic hamiltonian |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/210785 |
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