Mathematical Sciences: Flat Connections and Deformation Problems

数学科学：平面连接和变形问题

• 批准号: 9123844
• 负责人: David Sattinger
• 金额: $ 9万
• 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: 1992
• 资助国家: 美国
• 起止时间: 1992-07-01 至 1995-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9123844&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Flat; Connections; Deformation

The principal investigator will study isomonodromy deformation problems and their application to solve asymptotic connection formulae and to carry out a related study on the factorization problem associated with Gelfand-Dikii flows. These fundamental properties of integrable systems have been established for the 2 x 2 case, but have not been resolved for the general n x n case. A geometrical-analytical understanding is critical for further development. Integrable systems and inverse scattering problems play a fundamental role in establishing links between fundamental physics and the way in which mathematical models are used to describe it.

主要研究者将研究等单性变形问题及其在求解渐近连接公式中的应用，并对与 Gelfand-Dikii 流相关的因式分解问题进行相关研究。 可积系统的这些基本属性已针对 2 x 2 情况建立，但对于一般 n x n 情况尚未解决。 几何分析的理解对于进一步的发展至关重要。 可积系统和逆散射问题在建立基础物理与数学模型描述方式之间的联系方面发挥着重要作用。