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The Painleve Property : One Century Later :  One Century Later - Robert Conte

The Painleve Property : One Century Later

One Century Later

By: Robert Conte (Editor)


Published: September 1999
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The subject this volume is explicit integration, that is, the analytical as opposed to the numerical solution, of all kinds of nonlinear differential equations (ordinary differential, partial differential, finite difference). Such equations describe many physical phenomena, their analytic solutions (particular solutions, first integral, and so forth) are in many cases preferable to numerical computation, which may be long, costly and, worst, subject to numerical errors. In addition, the analytic approach can provide a global knowledge of the solution, while the numerical approach is always local. Explicit integration is based on the powerful methods based on an in-depth study of singularities, that were first used by Poincaré and subsequently developed by Painlevé in his famous Leçons de Stockholm of 1895. The recent interest in the subject and in the equations investigated by Painlevé dates back about thirty years ago, arising from three, apparently disjoint, fields: the Ising model of statistical physics and field theory, propagation of solitons, and dynamical systems. The chapters in this volume, based on courses given at Cargèse 1998, alternate mathematics and physics; they are intended to bring researchers entering the field to the level of present research.

Series Preface
Singularities of Ordinary Linear Differential Equations and Integrabilityp. 1
Introduction to the Theory of Isomonodromic Deformations of Linear Ordinary Differential Equations with Rational Coefficientsp. 35
The Painleve Approach to Nonlinear Ordinary Differential Equationsp. 77
Asymptotic Studies of the Painleve Equationsp. 181
2-D Quantum and Topological Gravities, Matrix Models, and Integrable Differential Systemsp. 229
Painleve Transcendents in Two-Dimensional Topological Field Theoryp. 287
Discrete Painleve Equationsp. 413
Painleve Analysis for Nonlinear Partial Differential Equationsp. 517
On Painleve and Darboux - Halphen-Type Equationsp. 573
Symmetry Reduction and Exact Solutions of Nonlinear Partial Differential Equationsp. 591
Painleve Equations in Terms of Entire Functionsp. 661
Backlund Transformations of Painleve Equations and Their Applicationsp. 687
The Hamiltonians Associated to the Painleve Equationsp. 735
"Completeness" of the Painleve Test - General Considerations - Open Problemsp. 789
Indexp. 805
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780387988887
ISBN-10: 0387988882
Series: CRM Series in Mathematical Physics
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 810
Published: September 1999
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 23.5 x 15.5  x 4.45
Weight (kg): 1.4