Recent Developments in Integrable Systems and Riemann-Hilbert Problems

by AMS Special Session Integrable Systems and Riemann-Hilbert Problems (University of Alabama : 2000); McLaughlin, Kenneth T-R

• ISBN13: 9780821832035
• ISBN10: 0821832034
• Format: Paperback
• Copyright: 2003-07-01
• Publisher: Amer Mathematical Society

Summary

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 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.

Table of Contents

Preface	p. vii
Riemann-Hilbert problems for last passage percolation	p. 1
Inverse scattering and some finite-dimensional integrable systems	p. 23
Recent results on second harmonic generation	p. 33
On long-distance intensity asymptotics of solutions to the Cauchy problem for the modified nonlinear Schrodinger equation for vanishing initial data	p. 49
Integrable models in Bose-Einstein condensates	p. 59
Long-time asymptotics of solutions to the Cauchy problem for the defocusing non-linear Schrodinger equation with finite-density initial data. I. Solitonless sector	p. 91
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