Overview
- Provides an accessible yet thorough introduction to Painlevé analysis
- Presents expanded, revised, and updated material with comprehensive coverage of both classical and modern applications
- Includes many diverse examples that are relevant to physical scientists
Part of the book series: Mathematical Physics Studies (MPST)
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About this book
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.
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Keywords
- Nevanlinna theory
- Painlevé test
- discrete nonlinear systems
- Korteweg-de Vries equation
- Hénon-Heiles Hamiltonian
- complex Ginzburg-Landau equation
- Kuramoto-Sivashinsky equation
- Kolmogorov-Petrovski-Piskunov equation
- Lorenz model of atmospheric circulation
- Bianchi IX cosmological model
- KdV equation
- KPP equation
- partial differential equations
Table of contents (9 chapters)
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Front Matter
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Back Matter
Reviews
“The new edition includes an overview of new results achieved since the first edition of the book, appendices, and comprehensive references. ‘The Painlevé 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)
Authors and Affiliations
About the authors
Robert Conte is associate director of research at the Centre de mathématiques et de leurs applications, École normale supérieure de Cachan, CNRS, Université Paris-Saclay. He is also an honorary professor in the Department of Mathematics at the University of Hong Kong, and an associate external member of the Centre de recherches mathématiques, Université de Montréal, Canada. He received his PhD from Université Paris VI and held positions at IBM France, UC Berkeley, and the Commissariat à l’énergie atomique, Saclay, before taking on his current role. He has co-authored and edited six books and published nearly 100 articles in refereed journals. Trained in both mathematics and physics, the main theme of his research is the mathematical solution of theoretical problems arising from physics.
Micheline Musette is professor emerita at the Vrije Universiteit, Dienst Theoretische Natuurkunde (TENA) Brussels, Belgium. Prior to joining the Vrije Universiteit, she completed 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.
Bibliographic Information
Book Title: The Painlevé Handbook
Authors: Robert Conte, Micheline Musette
Series Title: Mathematical Physics Studies
DOI: https://doi.org/10.1007/978-3-030-53340-3
Publisher: Springer Cham
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: Springer Nature Switzerland AG 2020
Hardcover ISBN: 978-3-030-53339-7Published: 08 November 2020
Softcover ISBN: 978-3-030-53342-7Published: 08 November 2021
eBook ISBN: 978-3-030-53340-3Published: 07 November 2020
Series ISSN: 0921-3767
Series E-ISSN: 2352-3905
Edition Number: 2
Number of Pages: XXXI, 389
Number of Illustrations: 9 b/w illustrations, 6 illustrations in colour
Additional Information: Jointly published with Canopus Publishing Limited, Bristol, UK
Topics: Mathematical Methods in Physics, Mathematical Physics, Partial Differential Equations, Dynamical Systems and Ergodic Theory, Mathematical and Computational Engineering, Math. Applications in Chemistry