English

On the Riemann-Hilbert problem for a $q$-difference Painlev\'e equation

Exactly Solvable and Integrable Systems 2021-01-20 v3 Mathematical Physics math.MP

Abstract

A Riemann-Hilbert problem for a qq-difference Painlev\'e equation, known as qPIVq\textrm{P}_{\textrm{IV}}, is shown to be solvable. This yields a bijective correspondence between the transcendental solutions of qPIVq\textrm{P}_{\textrm{IV}} and corresponding data on an associated qq-monodromy surface. We also construct the moduli space of qPIVq\textrm{P}_{\textrm{IV}} explicitly.

Keywords

Cite

@article{arxiv.1911.05854,
  title  = {On the Riemann-Hilbert problem for a $q$-difference Painlev\'e equation},
  author = {Nalini Joshi and Pieter Roffelsen},
  journal= {arXiv preprint arXiv:1911.05854},
  year   = {2021}
}

Comments

32 pages, 1 figure, bibliography updated and 1 reference added

R2 v1 2026-06-23T12:15:12.432Z