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JOURNALS // Symmetry, Integrability and Geometry: Methods and Applications // Archive

SIGMA, 2024 Volume 20, 087, 26 pp. (Mi sigma2089)

Algebraic Complete Integrability of the $a_4^{(2)}$ Toda Lattice

Bruce Lionnel Lietap Ndia, Djagwa Dehainsalab, Joseph Donghoa

a University of Maroua, Faculty of Sciences, Department of Mathematics Computer Sciences, P.O. Box 814, Maroua, Cameroon
b Department of Mathematics, Faculty of Exact and Applied Sciences, University of NDjamena, 1 route de Farcha, P.O. Box 1027, NDjamena, Chad

Abstract: The aim of this work is focused on the investigation of the algebraic complete integrability of the Toda lattice associated with the twisted affine Lie algebra $a_4^{(2)}$. 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.

Keywords: Toda lattice, integrable system, algebraic integrability, abelian surface.

MSC: 34G20, 34M55, 37J35

Received: April 25, 2024; in final form September 25, 2024; Published online October 5, 2024

Language: English

DOI: 10.3842/SIGMA.2024.087


ArXiv: 2404.13688


© Steklov Math. Inst. of RAS, 2025