Separation of Variables, Quasi-Trigonometric -Matrices and Generalized Gaudin Models
We construct two new one-parametric families of separated variables for the classical Lax-integrable Hamiltonian systems governed by a one-parametric family of non-skew-symmetric, non-dynamical (2)⊗(2)-valued quasi-trigonometric classical -matrices. We show that for all but one classical -matrices i...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2021 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2021
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/211354 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Separation of Variables, Quasi-Trigonometric -Matrices and Generalized Gaudin Models. Taras Skrypnyk. SIGMA 17 (2021), 069, 21 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862569070540357632 |
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| author | Skrypnyk, Taras |
| author_facet | Skrypnyk, Taras |
| citation_txt | Separation of Variables, Quasi-Trigonometric -Matrices and Generalized Gaudin Models. Taras Skrypnyk. SIGMA 17 (2021), 069, 21 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We construct two new one-parametric families of separated variables for the classical Lax-integrable Hamiltonian systems governed by a one-parametric family of non-skew-symmetric, non-dynamical (2)⊗(2)-valued quasi-trigonometric classical -matrices. We show that for all but one classical -matrices in the considered one-parametric families, the corresponding curves of separation differ from the standard spectral curve of the initial Lax matrix. The proposed scheme is illustrated by an example of separation of variables for = 2 quasi-trigonometric Gaudin models in an external magnetic field.
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| first_indexed | 2026-03-13T11:23:58Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211354 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-13T11:23:58Z |
| publishDate | 2021 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Skrypnyk, Taras 2025-12-30T15:54:20Z 2021 Separation of Variables, Quasi-Trigonometric -Matrices and Generalized Gaudin Models. Taras Skrypnyk. SIGMA 17 (2021), 069, 21 pages 1815-0659 2020 Mathematics Subject Classification: 14H70; 17B80; 37J35 arXiv:2107.08376 https://nasplib.isofts.kiev.ua/handle/123456789/211354 https://doi.org/10.3842/SIGMA.2021.069 We construct two new one-parametric families of separated variables for the classical Lax-integrable Hamiltonian systems governed by a one-parametric family of non-skew-symmetric, non-dynamical (2)⊗(2)-valued quasi-trigonometric classical -matrices. We show that for all but one classical -matrices in the considered one-parametric families, the corresponding curves of separation differ from the standard spectral curve of the initial Lax matrix. The proposed scheme is illustrated by an example of separation of variables for = 2 quasi-trigonometric Gaudin models in an external magnetic field. The author is grateful to the late Boris Dubrovin for the discussions. The work on this paper was partially supported by the Division of Physics and Astronomy of the NAS of Ukraine (Project No. 0117U000240). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Separation of Variables, Quasi-Trigonometric -Matrices and Generalized Gaudin Models Article published earlier |
| spellingShingle | Separation of Variables, Quasi-Trigonometric -Matrices and Generalized Gaudin Models Skrypnyk, Taras |
| title | Separation of Variables, Quasi-Trigonometric -Matrices and Generalized Gaudin Models |
| title_full | Separation of Variables, Quasi-Trigonometric -Matrices and Generalized Gaudin Models |
| title_fullStr | Separation of Variables, Quasi-Trigonometric -Matrices and Generalized Gaudin Models |
| title_full_unstemmed | Separation of Variables, Quasi-Trigonometric -Matrices and Generalized Gaudin Models |
| title_short | Separation of Variables, Quasi-Trigonometric -Matrices and Generalized Gaudin Models |
| title_sort | separation of variables, quasi-trigonometric -matrices and generalized gaudin models |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211354 |
| work_keys_str_mv | AT skrypnyktaras separationofvariablesquasitrigonometricmatricesandgeneralizedgaudinmodels |