Painlevé Transcendents: Their Asymptotics and Physical Applications

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Decio Levi, Pavel Winternitz
Springer Science & Business Media, 11 de nov. 2013 - 446 pàgines
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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Continguts

Integral Equations and Connection Formulae for
1
Continuous and Discrete Painlevé Equations
33
The Painlevé Transcendents as Nonlinear Special
49
Connection Results for the First Painlevé Equation
61
Turning Points of Linear Systems and Double
81
On the Linearization of the Third Painlevé Equation
97
Differential Equations with Fixed Critical Points
103
Unification of PDE and ODE Versions of Painlevé
125
The Painlevé Classification of Partial Differential
261
xiii
268
Differential Invariants Double Fibrations and Painlevé
271
The Painlevé Equations and the Dynkin Diagrams
299
Singularities and Symmetries of Nonlinear Evolution
315
On Reductions of SelfDual YangMills Equations
331
The Asymptotic Solution of the Stimulated Raman
345
Symmetry Reduction for the Stimulated Raman
353

Theorems and Conjectures
145
Riemann Double Waves Darboux Method and
163
Hirota Forms for the Six Painlevé Equations from
175
Flexibility in Applying the Painlevé Test
187
Insertion of the Darboux Transformation in
197
Symmetries and Painlevé Property of Equations in
211
The Singular Manifold Method
225
Painlevé Balances and Dressing Transformations
249
Stimulated Raman Scattering in the Transient Limit
361
Spin Systems Statistical Mechanics and Painlevé
377
Integrability of ChernSimonsHiggs Vortex Equations
393
Some Isomonodromy Problems in Hyperbolic Space
407
Physical Applications of Painlevé Type Equations
425
Participants
433
Subject Index
441
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