Year: 2025
Author: Yaru Xu, Minxin Jia, Xianguo Geng, Yunyun Zhai
East Asian Journal on Applied Mathematics, Vol. 15 (2025), Iss. 1 : pp. 80–112
Abstract
Resorting to the discrete zero-curvature equation and the Lenard recursion equations, a hierarchy of integrable semi-discrete nonlinear evolution equations is derived from a $3 \times 3$ matrix spectral problem with three potentials. Based on the characteristic polynomial of the Lax matrix for the hierarchy, a trigonal curve is introduced, and the properties of the corresponding three-sheeted Riemann surface are studied, including the genus, three kinds of Abelian differentials, Riemann theta functions. The asymptotic properties of the Baker-Akhiezer function and fundamental meromorphic functions defined on the trigonal curve are analyzed with the established theory of trigonal curves. As a result, finite genus solutions of the whole integrable semi-discrete nonlinear evolution hierarchy are obtained.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.2023-195.251023
East Asian Journal on Applied Mathematics, Vol. 15 (2025), Iss. 1 : pp. 80–112
Published online: 2025-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 33
Keywords: Integrable semi-discrete nonlinear evolution equation trigonal curve Baker-Akhiezer function finite genus solution.