Overview

This book is the first comprehensive treatment of Painleve 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 Painleve 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 transcen-dental solutions, Backlund transformations and higher order analogues, treated separately for each of these six equations. The final chapter offers a short overview of applications of Pain-leve equations, including an introduction to their discrete counterparts. Due to the present important role of Painleve 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.

Full Product Details

9783110173796

Table of Contents

Reviews

Few books concentrating on topics in Painleve equations have been published, especially in English, since the appearance of those equations in the beginning of the last century. For this reason, this book written by Gromak, Laine and Shimomura is valuable for those who wish to learn quickly the fundamental properties of Painleve equations without the need to refer to a large number of original papers on them [...] Zentralblatt fur Mathematik [...] due to the relatively elementary treatment of the complicated subject, the book under review will be able to attract the attention of specialists and young researchers. Mathematical Reviews

Few books concentrating on topics in Painleve equations have been published, especially in English, since the appearance of those equations in the beginning of the last century. For this reason, this book written by Gromak, Laine and Shimomura is valuable for those who wish to learn quickly the fundamental properties of Painleve equations without the need to refer to a large number of original papers on them [...] Humihiko Watanabe, Zentralblatt fur Mathematik [...] due to the relatively elementary treatment of the complicated subject, the book under review will be able to attract the attention of specialists and young researchers. Andrei A. Kapaev, Mathematical Reviews -Few books concentrating on topics in Painleve equations have been published, especially in English, since the appearance of those equations in the beginning of the last century. For this reason, this book written by Gromak, Laine and Shimomura is valuable for those who wish to learn quickly the fundamental properties of Painleve equations without the need to refer to a large number of original papers on them [...]-Humihiko Watanabe, Zentralblatt fur Mathematik -[...] due to the relatively elementary treatment of the complicated subject, the book under review will be able to attract the attention of specialists and young researchers.-Andrei A. Kapaev, Mathematical Reviews

Few books concentrating on topics in Painlev' equations have been published, especially in English, since the appearance of those equations in the beginning of the last century. For this reason, this book written by Gromak, Laine and Shimomura is valuable for those who wish to learn quickly the fundamental properties of Painlev' equations without the need to refer to a large number of original papers on them [...] Humihiko Watanabe, Zentralblatt fr Mathematik [...] due to the relatively elementary treatment of the complicated subject, the book under review will be able to attract the attention of specialists and young researchers. Andrei A. Kapaev, Mathematical Reviews Few books concentrating on topics in Painleve equations have been published, especially in English, since the appearance of those equations in the beginning of the last century. For this reason, this book written by Gromak, Laine and Shimomura is valuable for those who wish to learn quickly the fundamental properties of Painleve equations without the need to refer to a large number of original papers on them [...] Humihiko Watanabe, Zentralblatt fur Mathematik [...] due to the relatively elementary treatment of the complicated subject, the book under review will be able to attract the attention of specialists and young researchers. Andrei A. Kapaev, Mathematical Reviews -Few books concentrating on topics in Painleve equations have been published, especially in English, since the appearance of those equations in the beginning of the last century. For this reason, this book written by Gromak, Laine and Shimomura is valuable for those who wish to learn quickly the fundamental properties of Painleve equations without the need to refer to a large number of original papers on them [...]- Humihiko Watanabe, Zentralblatt fur Mathematik -[...] due to the relatively elementary treatment of the complicated subject, the book under review will be able to attract the attention of specialists and young researchers.- Andrei A. Kapaev, Mathematical Reviews

Few books concentrating on topics in Painleve equations have been published, especially in English, since the appearance of those equations in the beginning of the last century. For this reason, this book written by Gromak, Laine and Shimomura is valuable for those who wish to learn quickly the fundamental properties of Painleve equations without the need to refer to a large number of original papers on them [...] Humihiko Watanabe, Zentralblatt fur Mathematik [...] due to the relatively elementary treatment of the complicated subject, the book under review will be able to attract the attention of specialists and young researchers. Andrei A. Kapaev, Mathematical Reviews

Author Information

Dr. Valerii Gromak works at the Belarussian State University in Minsk, Belarussia. Ilpo Laine is Professor at the Mathematics Department of the University of Joensuu, Finland. Shun Shimomura is Professor at the Mathematics Department of Keio University, Yokohama, Japan.

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