dorsal/arxiv
View SchemaThe Painlev\'e approach to nonlinear ordinary differential equations
| Authors | R. Conte |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9710020 |
| URL | https://arxiv.org/abs/solv-int/9710020 |
Abstract
The ``Painlev\'e analysis'' is quite often perceived as a collection of tricks reserved to experts. The aim of this course is to demonstrate the contrary and to unveil the simplicity and the beauty of a subject which 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 ``Painlev\'e 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 Poincar\'e. A summary can be found at the beginning of each chapter.
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"abstract": "The ``Painlev\\\u0027e analysis\u0027\u0027 is quite often perceived as a collection of\ntricks reserved to experts. The aim of this course is to demonstrate the\ncontrary and to unveil the simplicity and the beauty of a subject which is in\nfact the theory of the (explicit) integration of nonlinear differential\nequations.\n To achieve our goal, we will not start the exposition with a more or less\nprecise ``Painlev\\\u0027e test\u0027\u0027. On the contrary, we will finish with it, after a\ngradual introduction to the rich world of singularities of nonlinear\ndifferential equations, so as to remove any cooking recipe.\n The emphasis is put on embedding each method of the test into the well known\ntheorem of perturbations of Poincar\\\u0027e. A summary can be found at the beginning\nof each chapter.",
"arxiv_id": "solv-int/9710020",
"authors": [
"R. Conte"
],
"categories": [
"solv-int",
"nlin.SI"
],
"title": "The Painlev\\\u0027e approach to nonlinear ordinary differential equations",
"url": "https://arxiv.org/abs/solv-int/9710020"
},
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