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  • Gebundenes Buch

This book, now in its second edition, introduces the singularity analysis of differential and difference equations via the Painlevé test and shows how Painlevé analysis provides a powerful algorithmic approach to building explicit solutions to nonlinear ordinary and partial differential equations. It is illustrated with integrable equations such as the nonlinear Schrödinger equation, the Korteweg-de Vries equation, Hénon-Heiles type Hamiltonians, and numerous physically relevant examples such as the Kuramoto-Sivashinsky equation, the Kolmogorov-Petrovski-Piskunov equation, and mainly the cubic…mehr

Produktbeschreibung
This book, now in its second edition, introduces the singularity analysis of differential and difference equations via the Painlevé test and shows how Painlevé analysis provides a powerful algorithmic approach to building explicit solutions to nonlinear ordinary and partial differential equations. It is illustrated with integrable equations such as the nonlinear Schrödinger equation, the Korteweg-de Vries equation, Hénon-Heiles type Hamiltonians, and numerous physically relevant examples such as the Kuramoto-Sivashinsky equation, the Kolmogorov-Petrovski-Piskunov equation, and mainly the cubic and quintic Ginzburg-Landau equations.

Extensively revised, updated, and expanded, this new edition includes: recent insights from Nevanlinna theory and analysis on both the cubic and quintic Ginzburg-Landau equations; a close look at physical problems involving the sixth Painlevé function; and an overview of new results since the book's original publication with special focus on finite difference equations. The book features tutorials, appendices, and comprehensive references, and will appeal to graduate students and researchers in both mathematics and the physical sciences.

Autorenporträt
d a PhD at Université Libre, Brussels, and held positions at the Inter University Institute for Nuclear Sciences and the National Fund for Scientific Research, Belgium. She has published around 60 papers in refereed journals, and is a member of the American Physical Society.

Rezensionen
From the reviews:

"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. ... 'The Painlevé 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 Painlevé 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 Painlevé 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 Painlevé 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)
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