Painleve Transcendents

I: Asymptotics of Painleve Transcendents, Connection Formulas, New Mathematical Features.- Integral Equations and Connection Formulae for the Painleve Equations.- Continuous and Discrete Painleve Equations.- The Painleve Transcendents as Nonlinear Special Functions.- Connection Results for the First Painleve Equation.- Turning Points of Linear Systems and Double Asymptotics of the Painleve Transcendents.- On the Linearization of the Third Painleve Equation.- II: Painleve Analysis and Integrability.- Differential Equations with Fixed Critical Points.- Unification of PDE and ODE Versions of Painleve Analysis into a Single Invariant Version.- Painleve Integrability: Theorems and Conjectures.- Riemann Double Waves, Darboux Method and the Painleve Property.- Hirota Forms for the Six Painleve Equations from Singularity Analysis.- Flexibility in Applying the Painleve Test.- Insertion of the Darboux Transformation in the Invariant Painleve Analysis of Nonlinear Partial Differential Equations.- Symmetries and Painleve Property of Equations in the Burger's Family.- The Singular Manifold Method.- III: Classification, Symmetries, Geometry, and Painleve Equations.- Painleve Balances and Dressing Transformations.- The Painleve Classification of Partial Differential Equations.- Differential Invariants, Double Fibrations and Painleve Equations.- The Painleve 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 Painleve V via the Boutroux Transformation.- Stimulated Raman Scattering in the Transient Limit.- Spin Systems, Statistical Mechanics and Painleve 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 Painleve Type Equations Quadratic in the Highest Derivatives.- Participants.- Author Index.