The Painlevé property for partial differential equations

John Weiss, M. Tabor, George Carnevale

Research output: Contribution to journalArticle

1615 Scopus citations

Abstract

In this paper we define the Painlevé property for partial differential equations and show how it determines, in a remarkably simple manner, the integrability, the Bäcklund transforms, the linearizing transforms, and the Lax pairs of three well-known partial differential equations (Burgers' equation, KdV equation, and the modified KdV equation). This indicates that the Painlevé property may provide a unified description of integrable behavior in dynamical systems (ordinary and partial differential equations), while, at the same time, providing an efficient method for determining the integrability of particular systems.

Original languageEnglish (US)
Pages (from-to)522-526
Number of pages5
JournalJournal of Mathematical Physics
Volume24
Issue number3
StatePublished - Dec 1 1982

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ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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