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Asymptotic Studies of the Painlevé Equations

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The Painlevé Property

Part of the book series: CRM Series in Mathematical Physics ((CRM))

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Abstract

The main aim of this chapter is to explain direct and natural rigorous methods for carrying out local and some global asymptotic studies near fixed singular points of the classical Painlevé equations. Such methods were first developed by Boutroux (around 1913). Here we review these methods and improve Boutroux’s results. Moreover, we show that these methods can also be used to obtain asymptotic behavior in other limits, e.g., when a parameter of the equation becomes large. The methods and results are illustrated here for the first and second Painlevé equations.

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Authors
  1. Nalini Joshi
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Editors and Affiliations

  1. Service de Physique de l’etat Condensé, CEA Saclay, F91191, Gif-sur-Yvette Cedex, France

    Robert Conte

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© 1999 Springer-Verlag New York, Inc.

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Joshi, N. (1999). Asymptotic Studies of the Painlevé Equations. In: Conte, R. (eds) The Painlevé Property. CRM Series in Mathematical Physics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1532-5_4

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  • DOI: https://doi.org/10.1007/978-1-4612-1532-5_4

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-98888-7

  • Online ISBN: 978-1-4612-1532-5

  • eBook Packages: Springer Book Archive

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