Application of the~trigonal curve to a~hierarchy of generalized Toda lattices
Teoretičeskaâ i matematičeskaâ fizika, Tome 215 (2023) no. 1, pp. 47-73
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Starting from the zero-curvature equation and Lenard recurrence relations, we derive a hierarchy of generalized Toda lattices. The trigonal curve is introduced through the Lax pair characteristic polynomial for the discrete hierarchy, from which a Dubrovin-type equation is established. Then the asymptotic behavior of the Baker–Akhiezer function and the meromorphic function is analyzed, and the divisors of the two functions are also discussed. Moreover, the Abel map is defined and the corresponding flows are straightened out on the Jacobian variety, such that the final algebro-geometric solutions of the hierarchy are calculated in terms of the Riemann theta function.
Keywords:
discrete matrix spectral problem, generalized Toda lattices, trigonal curve, algebro-geometric solutions.
@article{TMF_2023_215_1_a2,
author = {Qiulan Zhao and Caixue Li and Xinyue Li},
title = {Application of the~trigonal curve to a~hierarchy of generalized {Toda} lattices},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {47--73},
publisher = {mathdoc},
volume = {215},
number = {1},
year = {2023},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2023_215_1_a2/}
}
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Qiulan Zhao; Caixue Li; Xinyue Li. Application of the~trigonal curve to a~hierarchy of generalized Toda lattices. Teoretičeskaâ i matematičeskaâ fizika, Tome 215 (2023) no. 1, pp. 47-73. http://geodesic.mathdoc.fr/item/TMF_2023_215_1_a2/