Painlevé Handbook

Conte and Musette are recognized authorities in the area of Painlevé equations and the Painlevé property.

• From the contents1. Introduction. 2. Singularity structure in the complex plane, the Painlevé test. 3. Integrating ordinary differential equations. 4. Painlevé property and Painlevé test for partial differential equations. 5. From the test to explicit solutions of PDEs. 6. Quartic Hénon-Heiles Hamiltonian. 7. Discrete nonlinear equations. 8. FAQ (Frequently asked questions). A. The classical results of Painlevé and followers. B. Brief presentation of the elliptic functions. C. Basic introduction to the Nevanlinna theory. D. More on the Painlevé transcendents. E. The bilinear operator of Hirota. F. Algorithm for computing the Laurent series.

From the reviews: "The new monograph of the leading experts in the singularity analysis of differential equations provides a profound introduction to the Painleve property and related topics on the boundary between integrable and nonintegrable differential and difference models. ... 'The Painleve handbook' gives a new insight and is really useful for anyone interesting in the theory of integrable systems." (Andrei A. Kapaev, Zentrablatt MATH, Vol. 1153, 2009) "The main aim of Painleve and his coworkers was to discover new special functions defined by the differential equations they found. ... Overall, the book is very well written. It is clear that the authors mean for the book to be accessible, and they have succeeded. ... Conte and Musette have written an excellent introduction to some of the methods Painleve and his collaborators used and, more importantly, to how those methods are still relevant today. I highly recommend their handbook." (Bernard Deconinck, SIAM Review, Vol. 51 (3), 2009) "This is an excellent monograph and survey on methods of integration of a large number of nonlinear ODEs ... . One may say that this book is an important completion of some recent monographs on the Painleve topic ... . The extensive reference list consists of approximately 450 items. ... the authors succeed in giving a readable treatment of various methods such as the singularity confinement, the polynomial growth, etc." (Ilpo Laine, Mathematical Reviews, Issue 2009 i)