Geodesic
Algebraic Complete Integrability of the $a_4^{(2)}$ Toda Lattice
Symmetry, integrability and geometry: methods and applications, Tome 20 (2024) Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     author = {Bruce Lionnel Lietap Ndi and Djagwa Dehainsala and Joseph Dongho},
     title = {Algebraic {Complete} {Integrability} of the $a_4^{(2)}$ {Toda} {Lattice}},
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Bruce Lionnel Lietap Ndi; Djagwa Dehainsala; Joseph Dongho. Algebraic Complete Integrability of the $a_4^{(2)}$ Toda Lattice. Symmetry, integrability and geometry: methods and applications, Tome 20 (2024). http://geodesic.mathdoc.fr/item/SIGMA_2024_20_a86/

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