Algebraic Complete Integrability of the ⁽²⁾₄ Toda Lattice
This work aims to investigate the algebraic complete integrability of the Toda lattice associated with the twisted affine Lie algebra ⁽²⁾₄. First, we prove that the generic fiber of the momentum map for this system is an affine part of an abelian surface. Second, we show that the flows of integrable...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2024 |
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2024
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/212608 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Algebraic Complete Integrability of the ⁽²⁾₄ Toda Lattice. Bruce Lionnel Lietap Ndi, Djagwa Dehainsala and Joseph Dongho. SIGMA 20 (2024), 087, 26 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862540538113163264 |
|---|---|
| author | Lietap Ndi, Bruce Lionnel Dehainsala, Djagwa Dongho, Joseph |
| author_facet | Lietap Ndi, Bruce Lionnel Dehainsala, Djagwa Dongho, Joseph |
| citation_txt | Algebraic Complete Integrability of the ⁽²⁾₄ Toda Lattice. Bruce Lionnel Lietap Ndi, Djagwa Dehainsala and Joseph Dongho. SIGMA 20 (2024), 087, 26 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | This work aims to investigate the algebraic complete integrability of the Toda lattice associated with the twisted affine Lie algebra ⁽²⁾₄. First, we prove that the generic fiber of the momentum map for this system is an affine part of an abelian surface. Second, we show that the flows of integrable vector fields on this surface are linear. Finally, using the formal Laurent solutions of the system, we provide a detailed geometric description of these abelian surfaces and the divisor at infinity.
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| first_indexed | 2026-03-21T11:36:29Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212608 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-21T11:36:29Z |
| publishDate | 2024 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Lietap Ndi, Bruce Lionnel Dehainsala, Djagwa Dongho, Joseph 2026-02-09T08:05:46Z 2024 Algebraic Complete Integrability of the ⁽²⁾₄ Toda Lattice. Bruce Lionnel Lietap Ndi, Djagwa Dehainsala and Joseph Dongho. SIGMA 20 (2024), 087, 26 pages 1815-0659 2020 Mathematics Subject Classification: 34G20; 34M55; 37J35 arXiv:2404.13688 https://nasplib.isofts.kiev.ua/handle/123456789/212608 https://doi.org/10.3842/SIGMA.2024.087 This work aims to investigate the algebraic complete integrability of the Toda lattice associated with the twisted affine Lie algebra ⁽²⁾₄. First, we prove that the generic fiber of the momentum map for this system is an affine part of an abelian surface. Second, we show that the flows of integrable vector fields on this surface are linear. Finally, using the formal Laurent solutions of the system, we provide a detailed geometric description of these abelian surfaces and the divisor at infinity. We would like to extend our sincere gratitude to Professor Pol Vanhaecke at the University of Poitiers for his particular contributions, including clarifications and guidance on our research theme, and for the enriching exchanges and thoughtful advice he generously offered us throughout this project. We cannot end our acknowledgements without thanking all the referees of this paper. We wish to express our thanks to the referees for their valuable and helpful comments and suggestions. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Algebraic Complete Integrability of the ⁽²⁾₄ Toda Lattice Article published earlier |
| spellingShingle | Algebraic Complete Integrability of the ⁽²⁾₄ Toda Lattice Lietap Ndi, Bruce Lionnel Dehainsala, Djagwa Dongho, Joseph |
| title | Algebraic Complete Integrability of the ⁽²⁾₄ Toda Lattice |
| title_full | Algebraic Complete Integrability of the ⁽²⁾₄ Toda Lattice |
| title_fullStr | Algebraic Complete Integrability of the ⁽²⁾₄ Toda Lattice |
| title_full_unstemmed | Algebraic Complete Integrability of the ⁽²⁾₄ Toda Lattice |
| title_short | Algebraic Complete Integrability of the ⁽²⁾₄ Toda Lattice |
| title_sort | algebraic complete integrability of the ⁽²⁾₄ toda lattice |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212608 |
| work_keys_str_mv | AT lietapndibrucelionnel algebraiccompleteintegrabilityofthe24todalattice AT dehainsaladjagwa algebraiccompleteintegrabilityofthe24todalattice AT donghojoseph algebraiccompleteintegrabilityofthe24todalattice |