The Painlevé Handbook
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Beschreibung
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 thebook’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.
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.
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
Autor*in
Robert Conte
Themen in »The Painlevé Handbook«
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
Stimmen zu »The Painlevé Handbook«
“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)
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