This article is cited in 21 papers

Geometric Aspects of the Painlevé Equations $\mathrm{PIII(D_6)}$ and $\mathrm{PIII(D_7)}$

Marius van der Put, Jaap Top

Johann Bernoulli Institute, University of Groningen, P.O. Box 407, 9700 AK Groningen, The Netherlands

Abstract: The Riemann–Hilbert approach for the equations $\mathrm{PIII(D_6)}$ and $\mathrm{PIII(D_7)}$ is studied in detail, involving moduli spaces for connections and monodromy data, Okamoto–Painlevé varieties, the Painlevé property, special solutions and explicit Bäcklund transformations.

Keywords: moduli space for linear connections; irregular singularities; Stokes matrices; monodromy spaces; isomonodromic deformations; Painlevé equations.

MSC: 14D20; 14D22; 34M55

Received: October 15, 2013; in final form April 10, 2014; Published online April 23, 2014

Language: English

DOI: 10.3842/SIGMA.2014.050

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ArXiv: 1207.4023