Communications in Mathematical Physics

, Volume 91, Issue 3, pp 381–403 | Cite as

On the initial value problem of the second Painlevé Transcendent

  • A. S. Fokas
  • M. J. Ablowitz


The initial value problem associated with the second Painlevé Transcendent is linearized via a matrix, discontinuous, homogeneous Riemann-Hilbert (RH) problem defined on a complicated contour (six rays intersecting at the origin). This problem is mapped through a series of transformations to three different simple Riemann-Hilbert problems, each of which can be solved via a system of two Fredholm integral equations. The connection of these results with the inverse scattering transform in one and two dimensions is also pointed out.


Neural Network Statistical Physic Integral Equation Complex System Nonlinear Dynamics 
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Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • A. S. Fokas
    • 1
  • M. J. Ablowitz
    • 1
  1. 1.Department of Mathematics and Computer ScienceClarkson College of TechnologyPotsdamUSA

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