Families of linear differential equations related to the second Painlevé equation
Volume 94 / 2011
Banach Center Publications 94 (2011), 247-262
MSC: Primary 14D20; Secondary 14D22, 34M55.
DOI: 10.4064/bc94-0-18
Abstract
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.
