Families of linear differential equations related to the second Painlevé equation

Marius van der Put. "Families of linear differential equations related to the second Painlevé equation." Banach Center Publications 94.1 (2011): 247-262. <http://eudml.org/doc/282555>.

@article{MariusvanderPut2011,
abstract = {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.},
author = {Marius van der Put},
journal = {Banach Center Publications},
keywords = {moduli space for linear connections; irregular singularities; Stokes matrices; monodromy spaces; isomonodromic deformations; Painlevé equations; differential module; fine moduli space},
language = {eng},
number = {1},
pages = {247-262},
title = {Families of linear differential equations related to the second Painlevé equation},
url = {http://eudml.org/doc/282555},
volume = {94},
year = {2011},
}

TY - JOUR
AU - Marius van der Put
TI - Families of linear differential equations related to the second Painlevé equation
JO - Banach Center Publications
PY - 2011
VL - 94
IS - 1
SP - 247
EP - 262
AB - 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.
LA - eng
KW - moduli space for linear connections; irregular singularities; Stokes matrices; monodromy spaces; isomonodromic deformations; Painlevé equations; differential module; fine moduli space
UR - http://eudml.org/doc/282555
ER -