Communications in Mathematical Physics

, Volume 144, Issue 3, pp 601–622 | Cite as

On the solvability of Painlevé II and IV

  • A. S. Fokas
  • Xin Zhou
Article

Abstract

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 int solutions. Furthermore, for special relations among the monodromy data and fort on Stokes lines, these solutions are bounded for finitet.

Keywords

Differential Equation Neural Network Statistical Physic Complex System Ordinary Differential Equation 

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Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • A. S. Fokas
    • 1
  • Xin Zhou
    • 2
  1. 1.Department of Mathematics and Computer Science, Institute for Nonlinear SciencesClarkson UniversityPotsdamUSA
  2. 2.Department of MathematicsYale UniversityNew HavenUSA

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