关于第四个 $q$-Painlevé 方程的对称解
可精确求解与可积系统
2023-04-26 v2 经典分析与常微分方程
摘要
Painlevé 方程具有超越解 ，其在复 平面上在旋转或反射下具有特殊初值对称。它们对应于可用经典特殊函数显式求解的单调性问题。本文中，我们证明了一个 -差分 Painlevé 方程存在此类解。我们聚焦于被称为 或 的 -差分方程的对称解，给出其对称性质并求解相应的单调性问题。
引用
@article{arxiv.2212.11513,
title = {On symmetric solutions of the fourth $q$-Painlev\'e equation},
author = {Nalini Joshi and Pieter Roffelsen},
journal= {arXiv preprint arXiv:2212.11513},
year = {2023}
}
备注
27 pages, 7 figures. Parts of the text on the discrete symmetries $\mathcal{T}_{\pm}$ and their relation to the symmetry group updated, emphasising that both correspond to one and the same Dynkin diagram automorphism. The title of section 5 has been changed, typos have been fixed and other minor updates