Connection Problem of q-linear Equations and the q-Painlevé Third Equation

IF 1.2 3区数学 Q3 MATHEMATICS, APPLIED

Mathematical Physics, Analysis and Geometry Pub Date : 2026-10-05 DOI:10.1007/s11040-026-09593-9

Yousuke Ohyama

引用次数: 0

Abstract

We study the analytic properties of solutions to the q-Painlevé third equation. The q-Painlevé third equation can be represented as a connection preserving deformation of a linear q-difference equation. We investigate the connection problem for this linear q-difference equation and show that the connection matrix is expressed as a product of connection matrices arising from confluent q-hypergeometric equations.

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q-线性方程与q- painlelevel3方程的连接问题

研究了q- painlevel第三方程解的解析性质。q- painlevel第三方程可以表示为线性q差分方程的保持连接的变形。研究了线性q-差分方程的连接问题，并证明了连接矩阵可以表示为由合流q-超几何方程产生的连接矩阵的乘积。

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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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.