JournalsprimsVol. 39 , No. 3DOI 10.2977/prims/1145476076

A New Technique in Nonlinear Singularity Analysis

  • Andrew Pickering

    Universidad Rey Juan Carlos I, Móstoles (Madrid), Spain
  • Nalini Joshi

    The University of Sydney, Australia
  • Pilar R. Gordoa

    Universidad de Salamanca, Spain
A New Technique in Nonlinear Singularity Analysis cover


The test for singularity structure proposed by Ablowitz, Ramani and Segur (1980) has been widely used to obtain necessary conditions for non-linear ordinary differential equations (ODEs) to have the Painlev´ property. In this paper, we proe vide an example of an ODE for which this standard test breaks down in a new and surprising way. We show how to overcome the problems presented by this equation by developing a new technique based on regular singular points of bilinear equations.