# Painlevé Transcendents: The Riemann-Hilbert Approach

### About this Title

**Athanassios S. Fokas**, *Cambridge University, Cambridge, United Kingdom*, **Alexander R. Its**, *Indiana University-Purdue University Indianapolis, Indianapolis, IN*, **Andrei A. Kapaev** and **Victor Yu. Novokshenov**, *Russian Academy of Sciences, Ufa, Russia*

Publication: Mathematical Surveys and Monographs

Publication Year
2006: Volume 128

ISBNs: 978-0-8218-3651-4 (print); 978-1-4704-1355-2 (online)

DOI: http://dx.doi.org/10.1090/surv/128

MathSciNet review: MR2264522

MSC: Primary 33E17; Secondary 30E25, 34M50, 34M55, 37K15, 37K20

### Table of Contents

**Front/Back Matter**

**Chapters**

- 1. Systems of linear ordinary differential equations with rational coefficients. Elements of the general theory
- 2. Monodromy theory and special functions
- 3. Inverse monodromy problem and Riemann-Hilbert factorization
- 4. Isomonodromy deformations. The Painlevé equations
- 5. The isomonodromy method
- 6. Bäcklund transformations
- 7. Asymptotic solutions of the second Painlevé equation in the complex plane. Direct monodromy problem approach
- 8. Asymptotic solutions of the second Painlevé equation in the complex plane. Inverse monodromy problem approach
- 9. PII Asymptotics on the canonical six-rays. The purely imaginary case
- 10. PII Asymptotics on the canonical six-rays. real-valued case
- 11. PII Quasi-linear stokes phenomenon
- 12. PIII equation, an overview
- 13. Sine-Gordon reduction of PIII
- 14. Canonical four-rays. Real-valued solutions of SG-PIII
- 15. Canonical four-rays. Singular solutions of the SG-PIII
- 16. Asymptotics in the complex plane of the SG-PIII transcendent