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portada Painlevé Differential Equations in the Complex Plane (Degruyter Studies in Mathematics)
Type
Physical Book
Publisher
Author
Year
2002
Language
English
Pages
312
Format
Hardcover
ISBN
3110173794
ISBN13
9783110173796
Edition No.
2013
Categories

Painlevé Differential Equations in the Complex Plane (Degruyter Studies in Mathematics)

Ilpo Laine; Valerii I. Gromak; Shun Shimomura (Author) · De Gruyter · Hardcover

Painlevé Differential Equations in the Complex Plane (Degruyter Studies in Mathematics) - Ilpo Laine; Valerii I. Gromak; Shun Shimomura

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Synopsis "Painlevé Differential Equations in the Complex Plane (Degruyter Studies in Mathematics) "

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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