一类关于2属超椭圆曲线的新的离散可积系统

IF 0.9 3区数学 Q3 MATHEMATICS, APPLIED

Mathematical Physics, Analysis and Geometry Pub Date : 2025-02-25 DOI:10.1007/s11040-025-09501-7

Jing-Rui Wu, Xing-Biao Hu

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引用次数: 0

摘要

在离散Toda （HADT）方程和商-商-差（QQD）格式及其饥渴形式（hHADT方程和hQQD格式）的激励下，考虑与属二超椭圆曲线相关的二元正交多项式的行列式结构，导出了一类新的离散可积系统。相应的Lax对通过这类二元正交多项式的递推关系表示。与HADT和QQD病例以及hHADT和hQQD病例中考虑的1属曲线相比，我们的研究强调2属超椭圆曲线结构更丰富。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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

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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来源期刊

Mathematical Physics, Analysis and Geometry 数学-物理：数学物理

CiteScore

2.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： MPAG is a peer-reviewed journal organized in sections. Each section is editorially independent and provides a high forum for research articles in the respective areas. The entire editorial board commits itself to combine the requirements of an accurate and fast refereeing process. The section on Probability and Statistical Physics focuses on probabilistic models and spatial stochastic processes arising in statistical physics. Examples include: interacting particle systems, non-equilibrium statistical mechanics, integrable probability, random graphs and percolation, critical phenomena and conformal theories. Applications of probability theory and statistical physics to other areas of mathematics, such as analysis (stochastic pde''s), random geometry, combinatorial aspects are also addressed. The section on Quantum Theory publishes research papers on developments in geometry, probability and analysis that are relevant to quantum theory. Topics that are covered in this section include: classical and algebraic quantum field theories, deformation and geometric quantisation, index theory, Lie algebras and Hopf algebras, non-commutative geometry, spectral theory for quantum systems, disordered quantum systems (Anderson localization, quantum diffusion), many-body quantum physics with applications to condensed matter theory, partial differential equations emerging from quantum theory, quantum lattice systems, topological phases of matter, equilibrium and non-equilibrium quantum statistical mechanics, multiscale analysis, rigorous renormalisation group.