Some Analytical Aspects of the Theory of Integrable Systems

DMS-9801608 亚历山大河其 该研究项目的重点是分析方面的理论， 与Riemann-Hilbert和isomonodromy方法相关的可积系统。 考虑的问题包括渐近分析的 精确可解量子场的关联函数与统计 力学模型，随机矩阵和正交多项式理论中双标度极限的研究，Painleve和KdV型可积微分方程解的整体渐近分析。 可积系统理论是一个不断扩展的领域， 日益重要的作用，作为一个新的主要来源 现代数学的许多分支的分析和代数思想， 理论物理学同时，它也为企业提供了一个有效的分析工具 研究一些基本的数学模型， 在现代非线性科学的众多应用中起着核心作用 和技术具体而言，上述研究方向 处理数学模型，形成理论基础， 以下领域：凝聚态，高能和等离子体物理， 非线性流体动力学和高比特率电信系统。

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.