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