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.

首席研究者将研究等异构畸形的变形问题及其在解决渐近连接公式中的应用，并就与Gelfand-Dikii流有关的分解问题进行相关研究。 已经为2 x 2个情况建立了可集成系统的这些基本属性，但尚未解决一般的n x n情况。 几何分析理解对于进一步的发展至关重要。 可集成的系统和反向散射问题在建立基本物理学与使用数学模型来描述它之间的联系方面起着基本作用。