
Ebook Info
- Published: 2013
- Number of pages: 303 pages
- Format: PDF
- File Size: 1.58 MB
- Authors: Ilpo Laine
Description
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.
User’s Reviews
Editorial Reviews: Review Few books concentrating on topics in Painlevé 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 Painlevé equations without the need to refer to a large number of original papers on them […] Zentralblatt für 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 About the Author
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.
Reviews from Amazon users which were colected at the time this book was published on the website:
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Keywords
Free Download Painlevé Differential Equations in the Complex Plane (Degruyter Studies in Mathematics) in PDF format
Painlevé Differential Equations in the Complex Plane (Degruyter Studies in Mathematics) PDF Free Download
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Painlevé Differential Equations in the Complex Plane (Degruyter Studies in Mathematics) 2013 PDF Free Download
Download Painlevé Differential Equations in the Complex Plane (Degruyter Studies in Mathematics) PDF
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