On the solvability of Painlevé II and IV

Journal Article (Journal Article)

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.

Full Text

Duke Authors

Cited Authors

  • Fokas, AS; Zhou, X

Published Date

  • March 1, 1992

Published In

Volume / Issue

  • 144 / 3

Start / End Page

  • 601 - 622

Electronic International Standard Serial Number (EISSN)

  • 1432-0916

International Standard Serial Number (ISSN)

  • 0010-3616

Digital Object Identifier (DOI)

  • 10.1007/BF02099185

Citation Source

  • Scopus