Mathematical Sciences: Algebraic Methods in Nonlinear Problems

数学科学：非线性问题的代数方法

• 批准号: 8702758
• 负责人: David Sattinger
• 金额: $ 2.4万
• 依托单位: University of Minnesota Saint Paul
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-07-01 至 1989-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8702758&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Algebraic; Methods; Nonlinear

The topic of this research is the algebraic and geometric structure of integrable systems and the role of Lie algebras. An analytical interpretation of the bilinear identity, which plays a fundamental role in the theory of tau function, vertex operators, and field theoretic methods of the Kyoto school in integrable systems is sought. The investigator will study the relationship between the tau method and the dressing method of Zakharov and Shabat. Possible applications are an extensions of the theory of tau function to other integrable systems, including multidimensional problems. The study of integrable systems is aimed at improving our understanding the nature of certain physical phenomena that have the properties of energy preservation, such as solitons.

这项研究的主题是可整合系统的代数和几何结构以及Lie代数的作用。寻求对京都学校在tau功能，顶点操作员和现场理论方法中在综合系统中的tau函数理论，顶点操作员和现场理论方法中起着基本作用的分析解释。研究人员将研究tau方法与Zakharov和Shabat的敷料方法之间的关系。可能的应用是TAU函数理论的扩展，包括其他可集成系统，包括多维问题。 对整合系统的研究旨在改善我们的理解某些具有能量保存特性的物理现象的本质，例如孤子。