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- Title
A Riemann–Hilbert approach to Painlevé IV.
- Authors
van der Put, Marius; Top, Jaap
- Abstract
The methods of [vdP-Sa, vdP1, vdP2] are applied to the fourth Painlevé equation. One obtains a Riemann–Hilbert correspondence between moduli spaces of rank two connections on ℙ1and 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 ℙ1are introduced, inspired by the symmetric form for PIV, studied by M. Noumi and Y. Yamada.
- Subjects
PAINLEVE equations; RIEMANN-Roch theorems; MONODROMY groups; BACKLUND transformations; MATHEMATICAL symmetry
- Publication
Journal of Nonlinear Mathematical Physics, 2013, Vol 20, p165
- ISSN
1402-9251
- Publication type
Article
- DOI
10.1080/14029251.2013.862442