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Explicit Solutions of the Coupled Bogoyavlensky Lattice 1(2) Hierarchy

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Abstract

By means of the discrete zero curvature representation, the coupled Bogoyavlensky lattice 1(2) hierarchy related to a \(3\times 3\) matrix problem is derived. Resorting to the characteristic polynomial of Lax matrix for the lattice hierarchy, we introduce a trigonal curve \(\mathcal {K}_{m-1}\) of arithmetic genus \(m-1\) and construct the related Baker–Akhiezer function and meromorphic function. By analyzing the asymptotic expansion of the meromorphic function, the algebro-geometric solutions to the stationary coupled Bogoyavlensky lattice 1(2) are obtained. Moreover, the explicit theta function representations for the coupled Bogoyavlensky lattice hierarchy are given with the help of the Abelian differential.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Zhengzhou University, 100 Kexue Road, Zhengzhou, 450001, Henan, People’s Republic of China

    Xianguo Geng, Wei Liu & Bo Xue

  2. Department of Mathematics and Physics, Shijiazhuang Tiedao University, 17 Northeast, Second Inner Ring, Shijiazhuang, 050043, Hebei, People’s Republic of China

    Wei Liu

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  1. Xianguo Geng
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  2. Wei Liu
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Correspondence to Bo Xue.

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This work is supported by National Natural Science Foundation of China (Grant Nos. 11971442, 11931017, 11871440), Natural Science Foundation of Hebei Province (Grant No. A2020210005), Foundation of Hebei Education Department of China (Grant No. QN2018050)

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Geng, X., Liu, W. & Xue, B. Explicit Solutions of the Coupled Bogoyavlensky Lattice 1(2) Hierarchy. Results Math 76, 67 (2021). https://doi.org/10.1007/s00025-021-01379-5

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