A Fuchs Extension to the Painlevé Test

  • R. Conte
  • A. P. Fordy
  • A. Pickering
Conference paper
Part of the Springer Series in Nonlinear Dynamics book series (SSNONLINEAR)

Abstract

We present a recent improvement [1] to the Painlevé test such that negative resonances can be treated. To this end we demand that the general solution of both the given nonlinear equation and its linearisation be single valued. This gives rise to compatibility conditions for every integer resonance, whether positive or negative. We present two illustrative examples: a generalised Chazy, and an anharmonic oscillator and indicate some future directions.

Keywords

Manifold Soliton 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • R. Conte
    • 1
  • A. P. Fordy
    • 2
  • A. Pickering
    • 2
  1. 1.Service de physique de l’état condensé (DRECAM-SPEC)Centre d’études de SaclayGif-sur-Yvette CedexFrance
  2. 2.Department of Applied Mathematical Studies and Centre for Nonlinear StudiesUniversity of LeedsUK

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