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arXiv · 1612.03674

Isomonodromy for the Degenerate Fifth Painlev\'e Equation

Primitivo B. Acosta-Humánez·Marius van der Put·Jaap Top
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Abstract

This is a sequel to papers by the last two authors making the Riemann-Hilbert correspondence and isomonodromy explicit. For the degenerate fifth Painlev\'e equation, the moduli spaces for connections and for monodromy are explicitly computed. It is proven that the extended Riemann-Hilbert morphism is an isomorphism. As a consequence these equations have the Painlev\'e property and the Okamoto-Painlev\'e space is identified with a moduli space of connections. Using MAPLE computations, one obtains formulas for the degenerate fifth Painlev\'e equation, for the B\"acklund transformations.

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Primitivo B. Acosta-Humánez, Marius van der Put, Jaap Top. 2016-12-12. Isomonodromy for the Degenerate Fifth Painlev\'e Equation. https://doi.org/10.3842/sigma.2017.029

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