Painlevé Differential Equations in the Complex Plane

This book is the first comprehensive treatment of Painlevé differential equations in the complex plane. Starting with a rigorous presentation for the meromorphic nature of their solutions, the Nevanlinna theory will be applied to offer a detailed exposition of growth aspects and value distribution o...

Ausführliche Beschreibung

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Bibliographische Detailangaben
Hauptverfasser: Gromak, Valerii I, Laine, Ilpo, Shimomura, Shun
Format: E-Book Buch
Sprache:Englisch
Veröffentlicht: Germany De Gruyter 2008
Walter de Gruyter
Walter de Gruyter GmbH
Ausgabe:1
Schriftenreihe:De Gruyter Studies in Mathematics
Schlagworte:
Functions of complex variables
Komplexe Funktion
MATHEMATICS
MATHEMATICS / General
MATHEMATICS / Mathematical Analysis
Painlevé equations
Painlevé-Gleichung
Komplexe Funktion
Painlevé-Gleichung
ISBN:3110198096, 9783110198096, 9783110173796, 3110173794
Online-Zugang:Volltext
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Beschreibung
Zusammenfassung:This book is the first comprehensive treatment of Painlevé differential equations in the complex plane. Starting with a rigorous presentation for the meromorphic nature of their solutions, the Nevanlinna theory will be applied to offer a detailed exposition of growth aspects and value distribution of Painlevé transcendents. The subsequent main part of the book is devoted to topics of classical background such as representations and expansions of solutions, solutions of special type like rational and special transcendental solutions, Bäcklund transformations and higher order analogues, treated separately for each of these six equations. The final chapter offers a short overview of applications of Painlevé equations, including an introduction to their discrete counterparts. Due to the present important role of Painlevé equations in physical applications, this monograph should be of interest to researchers in both mathematics and physics and to graduate students interested in mathematical physics and the theory of differential equations.
Bibliographie:Includes bibliographical reference (p. [283]-299) and index
ISBN:3110198096
9783110198096
9783110173796
3110173794
DOI:10.1515/9783110198096