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


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.

Cite this article

Andrew Pickering, Nalini Joshi, Pilar R. Gordoa, A New Technique in Nonlinear Singularity Analysis. Publ. Res. Inst. Math. Sci. 39 (2003), no. 3, pp. 435–449

DOI 10.2977/PRIMS/1145476076