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arXiv · 1911.05854

On the Riemann-Hilbert problem for a $q$-difference Painlevé equation

Nalini Joshi·Pieter Roffelsen
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Abstract

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

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Nalini Joshi, Pieter Roffelsen. 2021-01-19. On the Riemann-Hilbert problem for a $q$-difference Painlevé equation. https://arxiv.org/abs/1911.05854

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