Families of linear differential equations related to the second Painlevé equation

Tom 94 / 2011

Marius van der Put Banach Center Publications 94 (2011), 247-262 MSC: Primary 14D20; Secondary 14D22, 34M55. DOI: 10.4064/bc94-0-18


This paper is a sequel to \cite{vdP-Sa} and \cite{vdP}. The two classes of differential modules $(0,-,3/2)$ and $(-,-,3)$, related to PII, are interpreted as fine moduli spaces. It is shown that these moduli spaces coincide with the Okamoto–Painlevé spaces for the given parameters. The geometry of the moduli spaces leads to a proof of the Painlevé property for PII in standard form and in the Flaschka–Newell form. The Bäcklund transformations, the rational solutions and the Riccati solutions for PII are derived from these moduli spaces.


  • Marius van der PutDepartment of Mathematics
    University of Groningen
    P.O. Box 800
    9700 AV Groningen, the Netherlands

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