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Families of linear differential equations related to the second Painlevé equation

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van der Put M.

Banach Center Publications

2011

tom 94

nr 1

247-262

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.

Ograniczanie wyników

1 Banach Center Publications

1 van der Put M.

1 2011

Wyniki wyszukiwania

Families of linear differential equations related to the second Painlevé equation