A Riemann–Hilbert approach to Painlevé IV

DOI

10.1080/14029251.2013.862442How to use a DOI?

Keywords

Moduli space for linear connections; Irregular singularities; Stokes matrices; Monodromy spaces; Isomonodromic deformations; Painlevé equations

Abstract

The methods of [vdP-Sa, vdP1, vdP2] are applied to the fourth Painlevéequation. One obtains a Riemann–Hilbert correspondence between moduli spaces of rank two connections on ℙ¹ and moduli spaces for the monodromy data. The moduli spaces for these connections are identified with Okamoto–Painlevé varieties and the Painlevé property follows. For an explicit computation of the full group of Bäcklund transformations, rank three connections on ℙ¹ are introduced, inspired by the symmetric form for PIV, studied by M. Noumi and Y. Yamada.

Copyright

© 2013 The Authors. Published by Atlantis Press and Taylor & Francis

Open Access

This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Marius van der Put
AU  - Jaap Top
PY  - 2021
DA  - 2021/01/06
TI  - A Riemann–Hilbert approach to Painlevé IV
JO  - Journal of Nonlinear Mathematical Physics
SP  - 165
EP  - 177
VL  - 20
IS  - Supplement 1
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2013.862442
DO  - 10.1080/14029251.2013.862442
ID  - vanderPut2021
ER  -