Some Analytical Aspects of the Theory of Integrable Systems

可积系统理论的一些分析方面

• 批准号: 9801608
• 负责人: Alexander Its
• 金额: $ 14.89万
• 依托单位: Indiana University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-07-01 至 2001-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9801608&HistoricalAwards=false
• 关键词: Some; Analytical; Aspects; Theory; Integrable

DMS-9801608 Alexander R. Its The research project is focused on the analytical aspects of the theory of integrable systems related to the Riemann-Hilbert and isomonodromy methods. The problems under consideration include the asymptotic analysis of the correlation functions of exactly solvable quantum field and statistical mechanics models, the investigation of the double scaling limits in the theory of random matrices and orthogonal polynomials, and the global asymptotic analysis of the solutions of integrable differential equations of the Painleve' and KdV types. The theory of integrable systems is an expanding area which plays an increasingly important role as one of the principal sources of new analytical and algebraic ideas for many branches of modern mathematics and theoretical physics. Simultaneously, it provides an efficient analytic tool for the study of some of the fundamental mathematical models which play a central role in numerous applications arising in modern nonlinear science and technology. Specifically, the research directions indicated above deal with the mathematical models which form the theoretical basis for the following fields: condensed matter, high energy and plasma physics, nonlinear hydrodynamics, and high bit-rate telecommunication systems.

DMS-9801608 Alexander R.它的研究项目集中在与Riemann-Hilbert和Isomonodromy方法相关的综合系统理论的分析方面。 所考虑的问题包括对准确溶解的量子场和统计力学模型的相关函数的渐近分析，随机矩阵和正交多项式理论中的双重缩放限制的研究，以及对parchleve类型的集成微分方程的求解的全局渐近分析。 综合系统的理论是一个扩展领域，它是现代数学和理论物理学许多分支的新分析和代数思想的主要来源之一。同时，它为研究一些基本数学模型提供了有效的分析工具，这些工具在现代非线性科学和技术中引起的许多应用中起着核心作用。具体而言，上面指示的研究方向涉及构成以下领域的理论基础的数学模型：凝结物质，高能量和血浆物理学，非线性流体动力学以及高率电信系统。