Painlevé Transcendents

I: Asymptotics of Painlevé Transcendents, Connection Formulas, New Mathematical Features.- Integral Equations and Connection Formulae for the Painlevé Equations.- Continuous and Discrete Painlevé Equations.- The Painlevé Transcendents as Nonlinear Special Functions.- Connection Results for the First Painlevé Equation.- Turning Points of Linear Systems and Double Asymptotics of the Painlevé Transcendents.- On the Linearization of the Third Painlevé Equation.- II: Painlevé Analysis and Integrability.- Differential Equations with Fixed Critical Points.- Unification of PDE and ODE Versions of Painlevé Analysis into a Single Invariant Version.- Painlevé Integrability: Theorems and Conjectures.- Riemann Double Waves, Darboux Method and the Painlevé Property.- Hirota Forms for the Six Painlevé Equations from Singularity Analysis.- Flexibility in Applying the Painlevé Test.- Insertion of the Darboux Transformation in the Invariant Painlevé Analysis of Nonlinear Partial Differential Equations.- Symmetries and Painlevé Property of Equations in the Burger’s Family.- The Singular Manifold Method.- III: Classification, Symmetries, Geometry, and Painlevé Equations.- Painlevé Balances and Dressing Transformations.- The Painlevé Classification of Partial Differential Equations.- Differential Invariants, Double Fibrations and Painlevé Equations.- The Painlevé Equations and the Dynkin Diagrams.- Singularities and Symmetries of Nonlinear Evolution Equations.- IV: Applications.- On Reductions of Self-Dual Yang-Mills Equations.- The Asymptotic Solution of the Stimulated Raman-Scattering Equation.- Symmetry Reduction for the Stimulated Raman Scattering Equations and the Asymptotics of Painlevé V via the Boutroux Transformation.- Stimulated Raman Scattering in theTransient Limit.- Spin Systems, Statistical Mechanics and Painlevé Functions.- Integrability of Chern-Simons-Higgs Vortex Equations and a Reduction of the Self-Dual Yang-Mills Equations to Three Dimensions.- Some Isomonodromy Problems in Hyperbolic Space.- Physical Applications of Painlevé Type Equations Quadratic in the Highest Derivatives.- Participants.- Author Index.