On the solvability of Painlevé II and IV

We introduce a rigorous methodology for studying the Riemann-Hilbert problems associated with certain integrable nonlinear ordinary differential equations. For concreteness we investigate the Painlevé II and Painlevé IV equations. We show that the Cauchy problems for these equations admit in general global, meromorphic in t solutions. Furthermore, for special relations among the monodromy data and for t on Stokes lines, these solutions are bounded for finite t. © 1992 Springer-Verlag.

Duke Scholars

Author Xin Zhou Mathematics