Geodesic
On the integrable symplectic map and the  $N$-soliton solution
Teoretičeskaâ i matematičeskaâ fizika, Tome 215 (2023) no. 1, pp. 74-96
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Three different types of polynomial expansions of the spectral function are used to introduce the Hamiltonian system and the symplectic map associated to the Toda lattice. The integrability of the symplectic map and the Darboux coordinates are discussed. Using the Darboux coordinates, the symplectic map is linearized, and the inversion problem is derived. Finally, inversion is used to provide the $N$-soliton solution for the Toda lattice.
Keywords: symplectic map, integrable system, Darboux coordinates
Mots-clés : inversion, soliton solution. 
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Leilei Shi; Dianlou Du. On the integrable symplectic map and the  $N$-soliton solution. Teoretičeskaâ i matematičeskaâ fizika, Tome 215 (2023) no. 1, pp. 74-96. http://geodesic.mathdoc.fr/item/TMF_2023_215_1_a3/

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