A New Technique in Nonlinear Singularity Analysis | Zendy

Pilar R. Gordoa | Zendy; Nalini Joshi | Zendy; Andrew Pickering | Zendy

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A New Technique in Nonlinear Singularity Analysis

Author(s) -

Pilar R. Gordoa,

Nalini Joshi,

Andrew Pickering

Publication year - 2003

Publication title -

publications of the research institute for mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.786

H-Index - 39

eISSN - 1663-4926

pISSN - 0034-5318

DOI - 10.2977/prims/1145476076

Subject(s) - mathematics , singularity , nonlinear system , mathematical analysis , physics , quantum mechanics

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 Painleve property. In this paper, we provide 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.

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