Abstract
While this school focuses on discrete integrable systems we feel it necessary, if only for reasons of comparison, to go back to fundamentals and introduce the basic notion of the Painlevé property for continuous systems together with a critical analysis of what is called the Painlevé test. The extension of the latter to what is called the poly-Painlevé test is also introduced. Finally we devote a lesson to the proof that the Painlevé equations do have the Painlevé property.
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Kruskal, M., Grammaticos, B., Tamizhmani, T. Three Lessons on the Painlevé Property and the Painlevé Equations. In: Grammaticos, B., Tamizhmani, T., Kosmann-Schwarzbach, Y. (eds) Discrete Integrable Systems. Lecture Notes in Physics, vol 644. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-40357-9_1
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DOI: https://doi.org/10.1007/978-3-540-40357-9_1
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