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.

本研究的主题是可积系统的代数和几何结构以及李代数的作用。在可积系统的tau函数理论、顶点算子理论和京都学派的场论方法中起着重要作用的双线性恒等式的解析解释。研究者将研究扎哈罗夫和沙巴特的陶法和穿衣法之间的关系。可能的应用是将函数理论扩展到其他可积系统，包括多维问题。对可积系统的研究旨在提高我们对某些具有能量保存特性的物理现象的本质的理解，例如孤子。