A Riemann–Hilbert approach to Painlevé IV

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