Description 
1 online resource (xxxi, 389 pages) : illustrations (some color) 
Series 
Mathematical physics studies, 09213767 

Mathematical physics studies, 09213767

Contents 
1. Introduction  2. Singularity analysis: Painlevé test  3. Integrating ordinary differential equations  4. Partial Differential Equations: Painlevé 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 Painlevé functions. A. The classical results of Painlevé and followers. B. More on the Painlevé 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 
Summary 
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 Kortewegde Vries equation, HénonHeiles type Hamiltonians, and numerous physically relevant examples such as the KuramotoSivashinsky equation, the KolmogorovPetrovskiPiskunov equation, and mainly the cubic and quintic GinzburgLandau equations. Extensively revised, updated, and expanded, this new edition includes: recent insights from Nevanlinna theory and analysis on both the cubic and quintic GinzburgLandau 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 
Bibliography 
Includes bibliographical references and index 
Notes 
Online resource; title from PDF title page (SpringerLink, viewed January 28, 2021) 
Subject 
Painlevé equations.


Mathematical physics.


Differential equations, Partial.


Dynamics.


Ergodic theory.


Engineering mathematics.


Chemometrics.


Chemometrics


Differential equations, Partial


Dynamics


Engineering mathematics


Ergodic theory


Mathematical physics


Physics

Form 
Electronic book

Author 
Musette, Micheline, author.

ISBN 
9783030533403 

3030533409 
