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 萨廷格 本课题研究哈密顿量 基于半单李代数作为规范的层次 平面连接理论 扁平连接出现在 众多的问题，如自对偶杨米尔斯 方程和微分几何中的嵌入问题。 一个 一种推广Sato无穷维Grassmannian的方法 Kadomtsev-Petviashvili hierachy的图片到nxn 层次结构，提出了基于逆的解决方案， 线上n × n一阶系统的散射问题。 研究了层次的共伴随作用 从规范变换和 与解相关的Riemann-Hilbert分解 n × n系统的逆散射问题 的方法 基于散射理论结果的公式化 在主束方面，和“穿衣方法”的 扎哈罗夫和沙巴特