Perturbative methods for the Painlevé test

Details Perturbative methods for the Painlevé test Perturbative methods for the Painlevé test

1998-12-04

arxiv.org/abs/solv-int/9812007v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

11 pages, no figure, standard Latex, to appear in the proceedings of ``Nonlinear dynamics: integrability and chaos'', Tiruchir

Scientific paper

There exist many situations where an ordinary differential equation admits a movable critical singularity which the test of Kowalevski and Gambier fails to detect. Some possible reasons are: existence of negative Fuchs indices, insufficient number of Fuchs indices, multiple family, absence of an algebraic leading order. Mainly giving examples, we present the methods which answer all these questions. They are all based on the theorem of perturbations of Poincar\'e and computerizable.

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