Families of linear differential equations related to the second Painlevé equation

• Autorzy: Marius van der Put
• Języki publikacji: EN

Abstrakty

EN

This paper is a sequel to [vdP-Sa] and [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.

Kategorie tematyczne

• 34M55: Painlev\'e and other special equations; classification, hierarchies;
• 14D20: Algebraic moduli problems, moduli of vector bundles
• 14D22: Fine and coarse moduli spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2011
• Tom: 94
• Numer: 1
• Strony: 247-262

Daty

wydano

2011

Twórcy

autor

Marius van der Put

• Department of Mathematics, University of Groningen, P.O. Box 800, 9700 AV Groningen, the Netherlands

Identyfikatory

DOI

10.4064/bc94-0-18