A Riemann-Hilbert approach to Painleve IV

被引：3

作者：

van der Put, Marius ^{[1
]}

Top, Jaap ^{[1
]}

机构：

[1] Univ Groningen, Johann Bernoulli Inst, NL-9700 AK Groningen, Netherlands

来源：

JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS | 2013年 / 20卷

关键词：

Moduli space for linear connections; Irregular singularities; Stokes matrices; Monodromy spaces; Isomonodromic deformations; Painleve equations; ORDINARY DIFFERENTIAL-EQUATIONS; DEFORMATION; GEOMETRY; MODULI; PAIRS;

D O I：

10.1080/14029251.2013.862442

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The methods of [vdP-Sa, vdP1, vdP2] are applied to the fourth Painleve equation. One obtains a Riemann-Hilbert correspondence between moduli spaces of rank two connections on P-1 and moduli spaces for the monodromy data. The moduli spaces for these connections are identified with Okamoto-Painleve varieties and the Painleve property follows. For an explicit computation of the full group of Backlund transformations, rank three connections on P-1 are introduced, inspired by the symmetric form for PIV, studied by M. Noumi and Y. Yamada.

引用

页码：165 / 177

页数：13

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