Workshop on Soliton Equations: Applications and Theory

NSF Award Abstract - DMS-0104337 Mathematical Sciences：Workshop on Soliton Equations：Applications and Theory Abstract 0104337 Carlson该奖项旨在资助参加2001年8月10日至12日在科罗拉多斯普林斯的科罗拉多大学举办的“Soliton Equations：Applications and Theory”研讨会的美国参与者（主要是年轻的研究人员和研究生）。该研讨会涉及理论和应用专家对孤子方程的跨学科研究。 强调光通信的非线性问题，特别是使用非线性薛定谔方程及其变形的建模和设计的长距离光纤通信系统。 其他应用的主题包括在其他光学问题中的孤立子，磁性薄膜和玻色-爱因斯坦凝聚的外观。 理论主题包括逆散射和逆谱理论的扩展到薛定谔或狄拉克型运营商，分析黎曼-希尔伯特问题的新方法，孤子方程与几何的连接，以及对孤子方程的亚纯或真实的解析解的新见解。自从最初发现Korteweg - de弗里斯方程与散射变换有关以来，孤子方程提供了一个名副其实的物理和数学惊奇的源泉。 该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，并为年轻研究人员提供了该领域的概述。该研讨会旨在进行跨学科的演示，将这些想法成功应用于物理问题，计算研究可以照亮应用并提出新的理论问题，以及新的理论结果。

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.