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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc94-0-18,
author = {Marius van der Put},
title = {Families of linear differential equations related to the second Painlev\'e equation},
journal = {Banach Center Publications},
volume = {95},
year = {2011},
pages = {247-262},
zbl = {1233.14009},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc94-0-18}
}
Marius van der Put. Families of linear differential equations related to the second Painlevé equation. Banach Center Publications, Tome 95 (2011) pp. 247-262. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc94-0-18/