Geodesic
Algebro-geometric integration of the~modified Belov--Chaltikian lattice hierarchy
Teoretičeskaâ i matematičeskaâ fizika, Tome 199 (2019) no. 2, pp. 235-256

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Using the Lenard recurrence relations and the zero-curvature equation, we derive the modified Belov–Chaltikian lattice hierarchy associated with a discrete $3\times3$ matrix spectral problem. Using the characteristic polynomial of the Lax matrix for the hierarchy, we introduce a trigonal curve $\mathcal{K}_{m-2}$ of arithmetic genus $m-2$. We study the asymptotic properties of the Baker–Akhiezer function and the algebraic function carrying the data of the divisor near $P_{\infty_1}$, $P_{\infty_2}$, $P_{\infty_3}$, and $P_0$ on $\mathcal{K}_{m-2}$. Based on the theory of trigonal curves, we obtain the explicit theta-function representations of the algebraic function, the Baker–Akhiezer function, and, in particular, solutions of the entire modified Belov–Chaltikian lattice hierarchy.
Keywords: modified Belov–Chaltikian lattice hierarchy, trigonal curve, quasiperiodic solution. 
@article{TMF_2019_199_2_a4,
     author = {X. Geng and J. Wei and X. Zeng},
     title = {Algebro-geometric integration of the~modified {Belov--Chaltikian} lattice hierarchy},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {235--256},
     publisher = {mathdoc},
     volume = {199},
     number = {2},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2019_199_2_a4/}
}
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X. Geng; J. Wei; X. Zeng. Algebro-geometric integration of the~modified Belov--Chaltikian lattice hierarchy. Teoretičeskaâ i matematičeskaâ fizika, Tome 199 (2019) no. 2, pp. 235-256. http://geodesic.mathdoc.fr/item/TMF_2019_199_2_a4/