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.

主要研究员将研究等单调变形问题及其在求解渐近连接公式中的应用，并对Gelfand-Dikii流的分解问题进行相关研究。这些可积系统的基本性质已经在2 × 2情况下建立起来了，但是对于一般的n × n情况还没有解决。对几何分析的理解对进一步的发展至关重要。可积系统和逆散射问题在基础物理和数学模型之间建立联系方面起着重要作用。