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Painleve Transcendents : Their Asymptotics and Physical Applications - Decio Levi

Painleve Transcendents

Their Asymptotics and Physical Applications

By: Decio Levi (Editor), Pavel Winternitz (Editor)

Hardcover Published: 30th June 1992
ISBN: 9780306440502
Number Of Pages: 446

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The NATO Advanced Research Workshop "Painleve Transcendents, their Asymp- totics and Physical Applications", held at the Alpine Inn in Sainte-Adele, near Montreal, September 2 -7, 1990, brought together a group of experts to discuss the topic and produce this volume. There were 41 participants from 14 countries and 27 lectures were presented, all included in this volume. The speakers presented reviews of topics to which they themselves have made important contributions and also re- sults of new original research. The result is a volume which, though multiauthored, has the character of a monograph on a single topic. This is the theory of nonlinear ordinary differential equations, the solutions of which have no movable singularities, other than poles, and the extension of this theory to partial differential equations. For short we shall call such systems "equations with the Painleve property". The search for such equations was a very topical mathematical problem in the 19th century. Early work concentrated on first order differential equations. One of Painleve's important contributions in this field was to develop simple methods applicable to higher order equations. In particular these methods made possible a complete analysis of the equation;; = f(y', y, x), where f is a rational function of y' and y, with coefficients that are analytic in x. The fundamental result due to Painleve (Acta Math.

Paul Painleve: Essential Biographical Data
Scientific Publications of Paul Painleve
Asymptotics of Painleve Transcendents, Connection Formulas, New Mathematical Features
Integral Equations and Connection Formulae for the Painleve Equationsp. 1
Continuous and Discrete Painleve Equationsp. 33
The Painleve Transcendents as Nonlinear Special Functionsp. 49
Connection Results for the First Painleve Equationp. 61
Turning Points of Linear Systems and Double Asymptotics of the Painleve Transcendentsp. 81
On the Linearization of the Third Painleve Equationp. 97
Painleve Analysis and Integrability
Differential Equations with Fixed Critical Pointsp. 103
Unification of PDE and ODE Versions of Painleve Analysis into a Single Invariant Versionp. 125
Painleve Integrability: Theorems and Conjecturesp. 145
Riemann Double Waves, Darboux Method and the Painleve Propertyp. 163
Hirota Forms for the Six Painleve Equations from Singularity Analysisp. 175
Flexibility in Applying the Painleve Testp. 187
Insertion of the Darboux Transformation in the
Invariant Painleve Analysis of Nonlinear Partial Differential Equationsp. 197
Symmetries and Painleve Property of Equations in the Burger's Familyp. 211
The Singular Manifold Methodp. 225
Classification, Symmetries, Geometry, and Painleve Equations
Painleve Balances and Dressing Transformationsp. 249
The Painleve Classification of Partial Differential Equationsp. 261
Differential Invariants, Double Fibrations and Painleve Equationsp. 271
The Painleve Equations and the Dynkin Diagramsp. 299
Singularities and Symmetries of Nonlinear Evolution Equationsp. 315
On Reductions of Self-Dual Yang-Mills Equationsp. 331
The Asymptotic Solution of the Stimulated Raman-Scattering Equationp. 345
Symmetry Reduction for the Stimulated Raman Scattering Equations and the Asymptotics of Painleve V via the Boutroux Transformationp. 353
Stimulated Raman Scattering in the Transient Limitp. 361
Spin Systems, Statistical Mechanics and Painleve Functionsp. 377
Integrability of Chem-Simons-Higgs Vortex Equations and a Reduction of the Self-Dual Yang-Mills Equations to Three Dimensionsp. 393
Some Isomonodromy Problems in Hyperbolic Spacep. 407
Physical Applications of Painleve Type Equations Quadratic in the Highest Derivativesp. 425
Participantsp. 433
Author Indexp. 437
Subject Indexp. 441
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780306440502
ISBN-10: 0306440504
Series: NATO Science Series B:
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 446
Published: 30th June 1992
Country of Publication: US
Dimensions (cm): 25.4 x 17.78  x 2.69
Weight (kg): 1.04

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