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The Painlevé handbook

2009-04-06

“The new monograph of the leading experts in the singularity analysis of differential equations provides a profound introduction to the Painlevé property and related topics on the boundary between integrable and nonintegrable differential and difference models. Explaining their point of view, the authors follow the principal line: first specify equations which pass or partially pass the Painlevé test for conditions which are assumed to be necessary for integrability, and then, using a singular part transformation and its extensions, integrate the obtained equation, or prove its integrability, or at least construct particular solutions to the equation,“

begins Andrei A. Kapaev's review of The Painlevé handbook [Dordrecht: Springer. (2008; Zbl 1153.34002)] by Robert M. Conte and Micheline Musette.

In the following, his outlines in about three pages the content of the eight main Chapters in details, thereby providing an extensive survey of the different aspects of the field in itself. He concludes:

“In spite of the presentation sometimes seems too technical, and the reading is not always easy, no doubts, ‘The Painlevé handbook’ gives a new insight and is really useful for anyone interesting in the theory of integrable systems.”


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