Abstract
Using the Lenard recurrence relations and the zero-curvature equation, we derive the modified Belov—Chaltikian lattice hierarchy associated with a discrete 3×3 matrix spectral problem. Using the characteristic polynomial of the Lax matrix for the hierarchy, we introduce a tri gonal curve Km−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 P0 on Km−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.
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This research was supported by the National Natural Science Foundation of China (Grant Nos. 11871440, 11331008, and 11601488).
Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 199, No. 2, pp. 235–256, May, 2019.
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Geng, X., Wei, J. & Zeng, X. Algebro-Geometric Integration of the Modified Belov—Chaltikian Lattice Hierarchy. Theor Math Phys 199, 675–694 (2019). https://doi.org/10.1134/S0040577919050052
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DOI: https://doi.org/10.1134/S0040577919050052