Non-Fuchsian extension to the Painlevé test

Details Non-Fuchsian extension to the Painlevé test Non-Fuchsian extension to the Painlevé test

1995-08-28

arxiv.org/abs/solv-int/9508003v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

15 pages, no figure, Latex, to appear in Physics Letters A

Scientific paper

10.1016/0375-9601(95)00602-Y

We consider meromorphic particular solutions of nonlinear ordinary
differential equations and perform a perturbation {\it \`a la} Poincar\'e
making their linearized equation non-Fuchsian at the movable pole and Fuchsian
at infinity. When the nonlinear equation possesses movable logarithms, they are
detected sooner than with the perturbative (Fuchsian) Painlev\'e test.

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