Painlevé Transcendents

Their Asymptotics and Physical Applications

  • Decio Levi
  • Pavel Winternitz

Part of the NATO ASI Series book series (NSSB, volume 278)

Table of contents

  1. Front Matter
    Pages i-xxvi
  2. Asymptotics of Painlevé Transcendents, Connection Formulas, New Mathematical Features

  3. Painlevé Analysis and Integrability

  4. Classification, Symmetries, Geometry, and Painlevé Equations

    1. N. M. Ercolani, H. Flaschka, L. Haine
      Pages 249-260
  5. Applications

  6. Back Matter
    Pages 433-446

About this book


The NATO Advanced Research Workshop "Painleve Transcendents, their Asymp­ totics and Physical Applications", held at the Alpine Inn in Sainte-Adele, near Montreal, September 2 -7, 1990, brought together a group of experts to discuss the topic and produce this volume. There were 41 participants from 14 countries and 27 lectures were presented, all included in this volume. The speakers presented reviews of topics to which they themselves have made important contributions and also re­ sults of new original research. The result is a volume which, though multiauthored, has the character of a monograph on a single topic. This is the theory of nonlinear ordinary differential equations, the solutions of which have no movable singularities, other than poles, and the extension of this theory to partial differential equations. For short we shall call such systems "equations with the Painleve property". The search for such equations was a very topical mathematical problem in the 19th century. Early work concentrated on first order differential equations. One of Painleve's important contributions in this field was to develop simple methods applicable to higher order equations. In particular these methods made possible a complete analysis of the equation ;; = f(y',y,x), where f is a rational function of y' and y, with coefficients that are analytic in x. The fundamental result due to Painleve (Acta Math.


19th century differential equation geometry mechanics ordinary differential equation partial differential equation spin statistical mechanics symmetry

Editors and affiliations

  • Decio Levi
    • 1
  • Pavel Winternitz
    • 2
  1. 1.Dipartimento di FisicaUniversita di Roma La SapienzaRomaItaly
  2. 2.Centre de recherches mathématiquesUniversité de MontréalMontréalCanada

Bibliographic information

  • DOI
  • Copyright Information Springer Science+Business Media New York 1992
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4899-1160-5
  • Online ISBN 978-1-4899-1158-2
  • Series Print ISSN 0258-1221
  • Buy this book on publisher's site