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The Painlevé Approach to Nonlinear Ordinary Differential Equations

  • Chapter
The Painlevé Property

Part of the book series: CRM Series in Mathematical Physics ((CRM))

Abstract

The “Painlevé analysis” is quite often perceived as a collection of tricks reserved to experts. The aim of this chapter is to demonstrate the contrary and to unveil the simplicity and the beauty of a subject that is, in fact, the theory of the (explicit) integration of nonlinear differential equations.

To achieve our goal, we will not start the exposition with a more or less precise “Painlevé test.” On the contrary, we will finish with it, after a gradual introduction to the rich world of singularities of nonlinear differential equations, so as to remove any cooking recipe.

The emphasis is put on embedding each method of the test into the well-known theorem of perturbations of Poincaré. A summary can be found at the beginning of each section.

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    Robert Conte

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Conte, R. (1999). The Painlevé Approach to Nonlinear Ordinary Differential Equations. In: Conte, R. (eds) The Painlevé Property. CRM Series in Mathematical Physics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1532-5_3

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