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On the Riemann-Hilbert problem for a $q$-difference Painlevé equation (1911.05854v3)
Published 13 Nov 2019 in nlin.SI, math-ph, and math.MP
Abstract: A Riemann-Hilbert problem for a $q$-difference Painlev\'e 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.