Lagrangian Multiform for Cyclotomic Gaudin Models
We construct a Lagrangian multiform for the class of cyclotomic (rational) Gaudin models by formulating its hierarchy within the Lie dialgebra framework of Semenov-Tian-Shansky and by using the framework of Lagrangian multiforms on coadjoint orbits. This provides the first example of a Lagrangian mu...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2024 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2024
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/212644 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Lagrangian Multiform for Cyclotomic Gaudin Models. Vincent Caudrelier, Anup Anand Singh and Benoît Vicedo. SIGMA 20 (2024), 100, 30 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862720155422818304 |
|---|---|
| author | Caudrelier, Vincent Singh, Anup Anand Vicedo, Benoît |
| author_facet | Caudrelier, Vincent Singh, Anup Anand Vicedo, Benoît |
| citation_txt | Lagrangian Multiform for Cyclotomic Gaudin Models. Vincent Caudrelier, Anup Anand Singh and Benoît Vicedo. SIGMA 20 (2024), 100, 30 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We construct a Lagrangian multiform for the class of cyclotomic (rational) Gaudin models by formulating its hierarchy within the Lie dialgebra framework of Semenov-Tian-Shansky and by using the framework of Lagrangian multiforms on coadjoint orbits. This provides the first example of a Lagrangian multiform for an integrable hierarchy whose classical -matrix is non-skew-symmetric and spectral parameter-dependent. As an important by-product of the construction, we obtain a Lagrangian multiform for the periodic Toda chain by choosing an appropriate realisation of the cyclotomic Gaudin Lax matrix. This fills a gap in the landscape of Toda models, as only the open and infinite chains had been previously cast into the Lagrangian multiform framework. A slightly different choice of realisation produces the so-called discrete self-trapping (DST) model. We demonstrate the versatility of the framework by coupling the periodic Toda chain with the DST model and by obtaining a Lagrangian multiform for the corresponding integrable hierarchy.
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| first_indexed | 2026-03-21T02:15:34Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212644 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-21T02:15:34Z |
| publishDate | 2024 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Caudrelier, Vincent Singh, Anup Anand Vicedo, Benoît 2026-02-09T09:31:43Z 2024 Lagrangian Multiform for Cyclotomic Gaudin Models. Vincent Caudrelier, Anup Anand Singh and Benoît Vicedo. SIGMA 20 (2024), 100, 30 pages 1815-0659 2020 Mathematics Subject Classification: 17B80; 37J35; 70H06 arXiv:2405.12837 https://nasplib.isofts.kiev.ua/handle/123456789/212644 https://doi.org/10.3842/SIGMA.2024.100 We construct a Lagrangian multiform for the class of cyclotomic (rational) Gaudin models by formulating its hierarchy within the Lie dialgebra framework of Semenov-Tian-Shansky and by using the framework of Lagrangian multiforms on coadjoint orbits. This provides the first example of a Lagrangian multiform for an integrable hierarchy whose classical -matrix is non-skew-symmetric and spectral parameter-dependent. As an important by-product of the construction, we obtain a Lagrangian multiform for the periodic Toda chain by choosing an appropriate realisation of the cyclotomic Gaudin Lax matrix. This fills a gap in the landscape of Toda models, as only the open and infinite chains had been previously cast into the Lagrangian multiform framework. A slightly different choice of realisation produces the so-called discrete self-trapping (DST) model. We demonstrate the versatility of the framework by coupling the periodic Toda chain with the DST model and by obtaining a Lagrangian multiform for the corresponding integrable hierarchy. The authors would like to thank the referees for their constructive feedback. A.A.S. is funded by the School of Mathematics EPSRC Doctoral Training Partnership Studentship (Project Reference Number 2704447). B.V. gratefully acknowledges the support of the Leverhulme Trust through a Leverhulme Research Project Grant (RPG-2021-154). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Lagrangian Multiform for Cyclotomic Gaudin Models Article published earlier |
| spellingShingle | Lagrangian Multiform for Cyclotomic Gaudin Models Caudrelier, Vincent Singh, Anup Anand Vicedo, Benoît |
| title | Lagrangian Multiform for Cyclotomic Gaudin Models |
| title_full | Lagrangian Multiform for Cyclotomic Gaudin Models |
| title_fullStr | Lagrangian Multiform for Cyclotomic Gaudin Models |
| title_full_unstemmed | Lagrangian Multiform for Cyclotomic Gaudin Models |
| title_short | Lagrangian Multiform for Cyclotomic Gaudin Models |
| title_sort | lagrangian multiform for cyclotomic gaudin models |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212644 |
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