Mathematical Sciences: Geometry of Integrable Systems

数学科学：可积系统的几何

• 批准号: 8901607
• 负责人: David Sattinger
• 金额: $ 8.6万
• 依托单位: University of Minnesota-Twin Cities
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-06-15 至 1992-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8901607&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Geometry; Integrable; Systems

8901607 Sattinger This project concerns the investigation of Hamiltonian hierachies based on semi-simple Lie algebras viewed as gauge theories of a flat connection. Flat connections arise in a multitude of problems, such as the self-dual Yang-Mills equations, and embedding problems in differential geometry. An approach to extending Sato's infinite dimensional Grassmannian picture of the Kadomtsev-Petviashvili hierachy to the nxn hierarchies is proposed, based on the solution of the inverse scattering problem for nxn first order systems on the line. The co-adjoint action for the hierachies is to be investigated from the point of view gauge transformations and the Riemann-Hilbert factorization associated with the solution of the inverse scattering problem for nxn systems. The approach is based on the formulation of the results of scattering theory in terms of principal bundles, and the "dressing method" of Zakharov and Shabat.

8901607 Sattinger这个项目涉及对基于半简单谎言的哈密顿式hierachies的调查，被视为平坦连接的规格理论。 平坦的连接出现在多种问题中，例如自动扬米尔方程，并嵌入差异几何形状中的问题。 基于该生产线上NXN的一阶系统的逆散射问题的解决方案，提出了一种将Sato将Kadomtsev-PetviaShvili Hierachy扩展到NXN层次结构的无限尺寸格拉曼尼亚图片的方法。 层次的共同接合作用应从观点量规变换和与NXN系统的反向散射问题解决方案相关的Riemann-Hilbert分解。 该方法基于散射理论结果的制定，从主束和Zakharov和Shabat的“敷料方法”。