This volume is a collection of papers presented at a special session on integrable systems and Riemann-Hilbert problems. The goal of the meeting was to foster new research by bringing together experts from different areas. Their contributions to the volume provide a useful portrait of the breadth and depth of integrable systems.

Topics covered include discrete Painlevé equations, integrable nonlinear partial differential equations, random matrix theory, Bose-Einstein condensation, spectral and inverse spectral theory, and last passage percolation models. In most of these articles, the Riemann-Hilbert problem approach plays a central role, which is powerful both analytically and algebraically.

The book is intended for graduate students and researchers interested in integrable systems and its applications.

Readership

Graduate students and researchers interested in integrable systems and its applications.

Table of Contents

• J. Baik -- Riemann-Hilbert problems for last passage percolation
• R. Beals, D. H. Sattinger, and J. Szmigielski -- Inverse scattering and some finite-dimensional integrable systems
• D. J. Kaup and H. Steudel -- Recent results on second harmonic generation
• M. Kovalyov and A. H. Vartanian -- On long-distance intensity asymptotics of solutions to the Cauchy problem for the modified nonlinear Schrödinger equation for vanishing initial data
• W. M. Liu and S. T. Chui -- Integrable models in Bose-Einstein condensates
• A. H. Vartanian -- Long-time asymptotics of solutions to the Cauchy problem for the defocusing non-linear Schrödinger equation with finite-density initial data. I. Solitonless sector