Riemann-Hilbert Problem and Integrable Systems

黎曼-希尔伯特问题和可积系统

• 批准号: 0602344
• 负责人: Xin Zhou
• 金额: $ 12.54万
• 依托单位: Duke University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-06-01 至 2010-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0602344&HistoricalAwards=false
• 关键词: Riemann; Hilbert; Problem; Integrable; Systems

AbstractZhouThis proposal project covers, perturbation theory for focusing NLS,multiple orthogonal polynomials, oscillatory Riemann-Hilbertproblems with nonanalytic phase, zero dispersion of focusing NLS,orthogonal rational functions, and Janossy densities in the randommatrix theory. All these problems require Riemann-Hilbert problemtechniques to study.This project is an effort to develop further the analytic aspectsand the interdisciplinary applications of the fruitful field of theRiemann--Hilbert problem method, with the balance between itsintellectual and educational merits. The study of Riemann--Hilbertproblem has applications in several areas of mathematics andmathematical physics, including partial differential equations,statistical mechanics and combinatorics.

本项目内容包括：聚焦非线性最小二乘的微扰理论、多重正交多项式、非解析相的振荡Riemann-Hilbert问题、聚焦非线性最小二乘的零色散、正交有理函数和随机矩阵理论中的Janossy密度。所有这些问题都需要Riemann-Hilbert问题方法来研究。本项目旨在进一步发展Riemann-Hilbert问题方法的分析方面和跨学科应用，平衡其智力和教育价值。Riemann-Hilbert问题的研究在数学和数学物理的许多领域都有应用，包括偏微分方程、统计力学和组合数学。