@Article{EAJAM-15-80,
author = {Xu , YaruJia , MinxinGeng , Xianguo and Zhai , Yunyun},
title = {Finite Genus Solutions to a Hierarchy of Integrable Semi-Discrete Equations},
journal = {East Asian Journal on Applied Mathematics},
year = {2025},
volume = {15},
number = {1},
pages = {80--112},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2079-7370},
doi = {https://doi.org/10.4208/eajam.2023-195.251023},
url = {http://global-sci.org/intro/article_detail/eajam/23742.html}
}