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. 435–449DOI 10.2977/PRIMS/1145476076