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
Datum:2024
Hauptverfasser: Lietap Ndi, Bruce Lionnel, Dehainsala, Djagwa, Dongho, Joseph
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут математики НАН України 2024
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
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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.
first_indexed 2026-03-21T11:36:29Z
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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