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Painlevé Equations and Associated Polynomials

  • Peter A. Clarkson
Chapter
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Part of the Developments in Mathematics book series (DEVM, volume 13)

Abstract

In this paper we are concerned with rational solutions and associated polynomials for the second, third and fourth Painlevé equations. These rational solutions are expressible as in terms of special polynomials. The structure of the roots of these polynomials is studied and it is shown that these have a highly regular structure.

Keywords

Rational Solution Monic Polynomial Seed Solution Nagoya Math Integer Coefficient 
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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • Peter A. Clarkson
    • 1
  1. 1.Institute of Mathematics, Statistics & Actuarial ScienceUniversity of KentCanterburyUK

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