Workshop on Soliton Equations: Applications and Theory

数学科学：孤子方程：应用与理论研讨会（Workshop on Soliton Equations: Applications and Theory）该奖项支持2001年8月10-12日在科罗拉多大学举行的孤子方程：应用与理论研讨会（Workshop on Soliton Equations: Applications and Theory）的美国参与者（主要是年轻研究人员和研究生）。研讨会包括由专家从理论和应用两方面对孤子方程进行跨学科的考察。强调了光通信的非线性问题，特别是非线性薛定谔方程及其变体在远距离光纤通信系统建模和设计中的应用。其他应用主题包括在其他光学问题中孤子的出现，磁性薄膜，以及玻色-爱因斯坦凝聚。理论主题包括逆散射和逆谱理论对薛定谔或狄拉克型算子的扩展，分析黎曼-希尔伯特问题的新方法，孤立子方程与几何的联系，以及对孤立子方程亚纯或实解析解的新见解。自从将Korteweg - de Vries方程与散射变换联系起来的最初发现以来，孤子方程提供了一个名副其实的物理和数学惊喜的源泉。本次研讨会为该领域的研究人员提供了一个交流新成果和新问题的机会，并为青年研究人员提供了一个概述该领域的机会。讲习班的目的是进行跨学科的介绍，将这些思想成功地应用于物理问题、能够阐明应用并提出新的理论问题的计算研究以及新的理论结果健康地结合起来。

NSF Award Abstract - DMS-0104337Mathematical Sciences: Workshop on Soliton Equations: Applications and TheoryAbstract0104337 CarlsonThis award supports U.S. participants (primarily young researchers and graduate students) in the Workshop on Soliton Equations: Applications and Theory, held at the University of Colorado, Colorado Springs, on August 10-12, 2001. The workshop involves interdisciplinary examination of soliton equations by experts in both theory and applications. Nonlinear problems of optical communications are emphasized, particularly the use of the nonlinear Schroedinger equation and its variants for the modeling and design of long distance fiber optic communication systems. Additional applied topics include the appearance of solitons in other optical problems, magnetic thin films, and Bose-Einstein condensates. Theoretical topics include extensions of inverse scattering and inverse spectral theory to Schroedinger or Dirac type operators, new methods of analyzing Riemann-Hilbert problems, connections of soliton equations with geometry, and new insights into meromorphic or real analytic solutions of soliton equations. Since the initial discoveries relating the Korteweg - de Vries equation to the scatteringtransform, soliton equations have provided a veritable fountain of physical and mathematical surprises. This workshop offers researchers in this field a chance to exchange new results and new problems, and it provides young researchers with an overview of the field. The workshop aims at interdisciplinary presentation, with a healthy mix of successful applications of the ideas to physical problems, computational studies which can illuminate applications and suggest new theoretical issues, and new theoretical results.