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The Painleve handbook

Conte, Robert.

The Painleve handbook

Record Type:	Electronic resources : Monograph/item
Title/Author:	The Painleve handbookby Robert Conte, Micheline Musette.
Author:	Conte, Robert.
other author:	Musette, Micheline.
Published:	Cham :Springer International Publishing :2020.
Description:	xxxi, 389 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Painleve equations.
Online resource:	https://doi.org/10.1007/978-3-030-53340-3
ISBN:	9783030533403$q(electronic bk.)

The Painleve handbook
Conte, Robert.

The Painleve handbook[electronic resource] /by Robert Conte, Micheline Musette. - Second edition. - Cham :Springer International Publishing :2020. - xxxi, 389 p. :ill. (some col.), digital ;24 cm. - Mathematical physics studies,0921-3767. - Mathematical physics studies..

1. Introduction -- 2. Singularity analysis: Painleve test -- 3. Integrating ordinary differential equations -- 4. Partial Differential Equations: Painleve test -- 5. From the test to explicit solutions of PDEs -- 6. Integration of Hamiltonian Systems -- 7. Discrete nonlinear equations -- 8. FAQ (Frequently asked questions) -- 9. Selected Problems Integrated by Painleve functions. A. The classical results of Painleve and followers. B. More on the Painleve transcendents. C. Brief presentation of the elliptic functions. D. Basic introduction to the Nevanlinna theory. E. The bilinear formalism. F. Algorithm for computing the Laurent series. Index.

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.

ISBN: 9783030533403$q(electronic bk.)

Standard No.: 10.1007/978-3-030-53340-3doiSubjects--Topical Terms:

308867
Painleve equations.

LC Class. No.: QC20.7.D5 / C668 2020

Dewey Class. No.: 518.6

The Painleve handbook
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505 0 $a 1. Introduction -- 2. Singularity analysis: Painleve test -- 3. Integrating ordinary differential equations -- 4. Partial Differential Equations: Painleve test -- 5. From the test to explicit solutions of PDEs -- 6. Integration of Hamiltonian Systems -- 7. Discrete nonlinear equations -- 8. FAQ (Frequently asked questions) -- 9. Selected Problems Integrated by Painleve functions. A. The classical results of Painleve and followers. B. More on the Painleve transcendents. C. Brief presentation of the elliptic functions. D. Basic introduction to the Nevanlinna theory. E. The bilinear formalism. F. Algorithm for computing the Laurent series. Index.
520 $a 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.
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