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 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.

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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 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.

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Painlevé Differential Equations in the Complex Plane

Painlevé Differential Equations in the Complex Plane

Painlevé Differential Equations in the Complex Plane

Painlevé Differential Equations in the Complex Plane

Hardcover(Reprint 2013)

$280.00 
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Overview

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.


Product Details

ISBN-13: 9783110173796
Publisher: De Gruyter
Publication date: 10/24/2002
Series: De Gruyter Studies in Mathematics , #28
Edition description: Reprint 2013
Pages: 311
Product dimensions: 6.69(w) x 9.45(h) x (d)
Age Range: 18 Years

About the Author

Dr. Valerii Gromak works at the Belarussian State Universityin 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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