Solitons, Riemannian Geometry, Spectral Theory Educational Tools

孤子、黎曼几何、谱理论教育工具

• 批准号: 9704613
• 负责人: Serguei Novikov
• 金额: $ 6万
• 依托单位: University of Maryland, College Park
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-09-01 至 2000-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9704613&HistoricalAwards=false
• 关键词: Solitons; Riemannian; Geometry; Spectral; Theory

9704613 Novikov This project lies in the interface of analysis, topology/geometry, and applied mathematics. Hamiltonian theory of hydrodynamical systems, and exactly solvable Schrodinger operators are to be investigated. The techniques to be used include solitons, asymptotic methods in nonlinear wave theory, Kac-Moody type Lie algebras, topological quantum field theories, and nonstandard symmetry for the spectral theory of low-dimensional Schrodinger operators. Hamiltonian systems are systems composed of many particles moving without friction and are governed by a complicated system of differential equations. Hamiltonian theory simplifies these differential equations by first looking at the total energy of the system and often reveals hidden symmetries in the system. Dynamical systems model various phenomena in nature such as water waves and weather systems.

9704613 Novikov 该项目涉及分析、拓扑/几何和应用数学的接口。流体动力系统的哈密顿理论和精确可解的薛定谔算子有待研究。所使用的技术包括孤子、非线性波动理论中的渐近方法、Kac-Moody 型李代数、拓扑量子场论以及低维薛定谔算子谱理论的非标准对称性。 哈密​​顿系统是由许多无摩擦运动的粒子组成的系统，并受复杂的微分方程组控制。哈密​​顿理论通过首先观察系统的总能量来简化这些微分方程，并且经常揭示系统中隐藏的对称性。动力系统模拟自然界中的各种现象，例如水波和天气系统。