NATO Science Series B

Their Asymptotics and Physical Applications

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

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Hardcover | 30 June 1992

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476 Pages

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25.4 x 17.78 x 2.69

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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.

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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 Equations	p. 1
Continuous and Discrete Painleve Equations	p. 33
The Painleve Transcendents as Nonlinear Special Functions	p. 49
Connection Results for the First Painleve Equation	p. 61
Turning Points of Linear Systems and Double Asymptotics of the Painleve Transcendents	p. 81
On the Linearization of the Third Painleve Equation	p. 97
Painleve Analysis and Integrability
Differential Equations with Fixed Critical Points	p. 103
Unification of PDE and ODE Versions of Painleve Analysis into a Single Invariant Version	p. 125
Painleve Integrability: Theorems and Conjectures	p. 145
Riemann Double Waves, Darboux Method and the Painleve Property	p. 163
Hirota Forms for the Six Painleve Equations from Singularity Analysis	p. 175
Flexibility in Applying the Painleve Test	p. 187
Insertion of the Darboux Transformation in the
Invariant Painleve Analysis of Nonlinear Partial Differential Equations	p. 197
Symmetries and Painleve Property of Equations in the Burger's Family	p. 211
The Singular Manifold Method	p. 225
Classification, Symmetries, Geometry, and Painleve Equations
Painleve Balances and Dressing Transformations	p. 249
The Painleve Classification of Partial Differential Equations	p. 261
Differential Invariants, Double Fibrations and Painleve Equations	p. 271
The Painleve Equations and the Dynkin Diagrams	p. 299
Singularities and Symmetries of Nonlinear Evolution Equations	p. 315
Applications
On Reductions of Self-Dual Yang-Mills Equations	p. 331
The Asymptotic Solution of the Stimulated Raman-Scattering Equation	p. 345
Symmetry Reduction for the Stimulated Raman Scattering Equations and the Asymptotics of Painleve V via the Boutroux Transformation	p. 353
Stimulated Raman Scattering in the Transient Limit	p. 361
Spin Systems, Statistical Mechanics and Painleve Functions	p. 377
Integrability of Chem-Simons-Higgs Vortex Equations and a Reduction of the Self-Dual Yang-Mills Equations to Three Dimensions	p. 393
Some Isomonodromy Problems in Hyperbolic Space	p. 407
Physical Applications of Painleve Type Equations Quadratic in the Highest Derivatives	p. 425
Participants	p. 433
Author Index	p. 437
Subject Index	p. 441
Table of Contents provided by Blackwell. All Rights Reserved.

NATO Science Series B

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Hardcover

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