A Novel Discrete Integrable System Related to Hyper-Elliptic Curves of Genus Two

被引：0
|
作者：
Wu, Jing-Rui [1 ,2 ]
Hu, Xing-Biao [1 ,2 ]
机构：
[1] Chinese Acad Sci, LSEC, ICMSEC, Acad Math & Syst Sci, Beijing 100190, Peoples R China
[2] Univ Chinese Acad Sci, Sch Math Sci, Beijing 100190, Peoples R China
来源：
MATHEMATICAL PHYSICS ANALYSIS AND GEOMETRY | 2025年 / 28卷 / 01期
基金：
中国国家自然科学基金;
关键词：
Hyper-elliptic curves; Bivariate orthogonal polynomials; Discrete integrable systems; Lax pair; CONVERGENCE ACCELERATION ALGORITHM; LOTKA-VOLTERRA SYSTEM; ORTHOGONAL POLYNOMIALS; SHANKS TRANSFORMATION; TODA CHAIN; EQUATION; LATTICES;
D O I：
10.1007/s11040-025-09501-7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Motivated by the discrete-time Toda (HADT) equation and quotient-quotient-difference (QQD) scheme together with their hungry forms (hHADT equation and hQQD scheme), we derive a new class of discrete integrable systems by considering the determinant structures of bivariate orthogonal polynomials associated with the genus-two hyper-elliptic curves. The corresponding Lax pairs are expressed through the recurrence relations of this class of bivariate orthogonal polynomials. Our study emphasizes the richer structures of genus-two hyper-elliptic curves, in contrast to the genus-one curve considered in the HADT and QQD cases, as well as in the hHADT and hQQD cases.
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页数：22
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