The Painleve Handbook

By: Micheline Musette, Robert Conte

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Paperback | 8 November 2021 | Edition Number 2

At a Glance

Paperback
424 Pages

Edition Type
Revised

Dimensions(cm)
23.5 x 15.5 x 2.18

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$249.00

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This book, now in its second edition, introduces the singularity analysis of differential and difference equations via the Painleve test and shows how Painleve 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 Schrodinger equation, the Korteweg-de Vries equation, Henon-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 Painleve 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.

Industry Reviews

"The new edition includes an overview of new results achieved since the first edition of the book, appendices, and comprehensive references. 'The Painlev© handbook' will be useful for anyone interested in the theory of integrable nonlinear differential equations and systems, as well as for graduate students and researchers in both mathematics and physical sciences." (V. A. Pron'ko, zbMATH 1489.34001, 2022)

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