Painlevé Transcendents: Their Asymptotics and Physical ApplicationsDecio 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. |
Continguts
1 | |
Continuous and Discrete Painlevé Equations 33 | 32 |
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 |
XIII | 268 |
Differential Invariants Double Fibrations and Painlevé | 271 |
J Hurtubise and N Kamran | 297 |
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 |
Stimulated Raman Scattering in the Transient Limit | 361 |
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 |
The Painlevé Classification of Partial Differential | 261 |
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 |
437 | |
441 | |
Altres edicions - Mostra-ho tot
Painlevé Transcendents: Their Asymptotics and Physical Applications Decio Levi,Pavel Winternitz Visualització de fragments - 1992 |
Painlevé Transcendents: Their Asymptotics and Physical Applications Decio Levi,Pavel Winternitz Previsualització no disponible - 2013 |
Frases i termes més freqüents
7-function A₁ Ablowitz algebraic analytic asymptotic Bäcklund transformations behavior coefficients complex Comptes rendus condition consider constant corresponding Darboux Darboux transformation defined deformation denote derivatives dimensional équations différentielles expansion exponential field theory finite given Hamiltonian hyperbolic independent variable integral equation invariant inverse scattering Ising model isomonodromic Jimbo KdV equation Kruskal l'Académie des Sciences Lax pair Lett linear Math Mathematics matrix McCoy method monodromy movable singularities nonlinear obtain operator ordinary differential equations Painlevé analysis Painlevé equations Painlevé functions Painlevé property Painlevé test Painlevé Transcendents parameter partial differential equations Phys physical poles polynomial problem reduction rendus de l'Académie resonance Riemann satisfies SDYM second order Segur singular manifold singular points solitons solution solved symmetries theorem Toda lattice values Weiss Winternitz zero მ მ