Work

Monodromy and Isomonodromy for Linear $q$-Difference Systems with Coefficient Matrix $Ax+B$

Year: 2026

Type: preprint

Abstract: In this paper, we construct canonical fundamental solutions for linear $q$-difference systems with coefficient matrix $Ax+B$, develop the associated isomonodromy theory, and study the differential limit as $q\to1$. We determine the asymptotic behavior of generic isomonodromic deformations, and derive explicit formulas for their monodromy data in terms of their asymptotic leading terms. We also show that the differential limit as $q\to1$ recovers the canonical fundamental solutions, the monodromy data, and the isomonodromic deformations of the corresponding differential systems.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2608.29520

Authors: Lin, Jinghong, Tang, Qian, Xu, Xiaomeng

Institutions: Tsinghua University, Chinese Academy of Sciences, Peking University, Academy of Mathematics and Systems Science

Language: English

Topic: Nonlinear Waves and Solitons

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funder: National Key Research and Development Program of China

Award: G6601964384

OpenAlex ID: W7204890021

Cites: 5

Cited by:

Related to: 10