Painlevé Equations and Related Topics

Frontmatter

Preface

Contents

Part I. Plane Power Geometry

Chapter 1. Plane Power Geometry for One ODE and P1-P6
Chapter 2. New Simple Exact Solutions to Equation P6
Chapter 3. Convergence of a Formal Solution to an ODE
Chapter 4. Asymptotic Expansions and Forms of Solutions to P6
Chapter 5. Asymptotic Expansions of Solutions to P5

Part II. Space Power Geometry

Chapter 6. Space Power Geometry for one ODE and P1-P4, P6
Chapter 7. Elliptic and Periodic Asymptotic Forms of Solutions to P5
Chapter 8. Regular Asymptotic Expansions of Solutions to One ODE and P1-P5

Part III. Isomondromy Deformations

Chapter 9. Isomonodromic Deformations on Riemann Surfaces
Chapter 10. On Birational Darboux Coordinates of Isomonodromic Deformation Equations Phase Space
Chapter 11. On the Malgrange Isomonodromic Deformations of Nonresonant Irregular Systems
Chapter 12. Critical behavior of P6 Functions from the Isomonodromy Deformations Approach
Chapter 13. Isomonodromy Deformation of the Heun Class Equation
Chapter 14. Isomonodromy Deformations and Hypergeometric-Type Systems
Chapter 15. A Monodromy Problem Connected with P6
Chapter 16. Monodromy Evolving Deformations and Confluent Halphen's Systems
Chapter 17. On the Gauge Transformation of the Sixth Painlevé Equation
Chapter 18. Expansions for Solutions of the Schlesinger Equation at a Singular Point

Part IV. Painlevé Property

Chapter 19. Painleve Analysis of Lotka-Volterra Equations
Chapter 20. Painlevé Test and Briot-Bouquet Systems
Chapter 21. Solutions of the Chazy System
Chapter 22. Third-Order Ordinary Differential Equations with the Painlevé Test
Chapter 23. Analytic Properties of Solutions of a Class of Third-Order Equations with an Irrational Right-Hand Side

Part V. Other Aspects

Chapter 24. The Sixth Painlevé Transcendent and Uniformizable Orbifolds
Chapter 25. On Uniformizable Representation for Abelian Integrals
Chapter 26. Phase Shift for a Special Solution to the Korteweg-de Vries Equation in the Whitham Zone
Chapter 27. Fuchsian Reduction of Differential Equations
Chapter 28. The Voros Coefficient and the Parametric Stokes Phenomenon for the Second Painlevé Equation
Chapter 29. Integral Symmetry and the Deformed Hypergeometric Equation
Chapter 30. Integral Symmetries for Confluent Heun Equations and Symmetries of Painlevé Equation P5
Chapter 31. From the Tau Function of Painlevé P6 Equation to Moduli Spaces
Chapter 32. On particular Solutions of q-Painlevé Equations and q-Hypergeometric Equations
Chapter 33. Derivation of Painlevé Equations by Antiquantization
Chapter 34. Integral Transformation of Heun's Equation and Apparent Singularity
Chapter 35. Painlevé Analysis of Solutions to Some Nonlinear Differential Equations and their Systems Associated with Models of the Random-Matrix Type
Chapter 36. Reductions on the Lattice and Painlevé Equations P2, P5, P6

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