On symmetric solutions of the fourth $q$-Painlev\'e equation
Abstract
The Painlev\'e equations possess transcendental solutions with special initial values that are symmetric under rotation or reflection in the complex -plane. They correspond to monodromy problems that are explicitly solvable in terms of classical special functions. In this paper, we show the existence of such solutions for a -difference Painlev\'e equation. We focus on symmetric solutions of a -difference equation known as or and provide their symmetry properties and solve the corresponding monodromy problem.
Keywords
Cite
@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}
}
Comments
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