Integrability and the Painlevé property for low-dimensional systems

A. Ramani, B. Dorizzi, B. Grammaticos, T. Bountis

Research output: Contribution to journalArticlepeer-review

19 Citations (Scopus)


We examine a system described by two first-order nonlinear differential equations from the point of view of integrability. The singularity analysis in the complex-time plane is used to investigate the Painlevé property, which according to the Ablowitz-Ramani-Segur conjecture is a prerequisite for integrability for infinite-dimensional systems. We show that for such low-dimensional systems, the Painlevé analysis is still a most useful guide, but integrable cases also exist which do not possess the Painlevé property.

Original languageEnglish
Pages (from-to)878-883
Number of pages6
JournalJournal of Mathematical Physics
Issue number4
Publication statusPublished - 1984

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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