Mathematical Sciences: Aspects of Integrability

数学科学：可积性方面

• 批准号: 9204075
• 负责人: Athanassios Fokas
• 金额: $ 1.6万
• 依托单位: Clarkson University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-08-01 至 1995-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9204075&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Aspects; Integrability

The principal investigator will study nonlinear phenomena in which chaotic and solitonic behavior occur. Topics to be studied include Hamiltonian theory over non-commutative rings, algebraic and analytical aspects of the D-bar method, solutions of algebraic equations using algebraic geometric methods, Painleve equations and their appearance in the matrix models of quantum gravity, and generalizations of the hypergeometric functions. 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.

首席研究员将研究非线性现象 发生混沌和孤子行为。 研究课题 包括非交换环上Hamilton理论、代数 和分析方面的D-酒吧的方法，解决方案， 代数方程使用代数几何方法，Painleve 方程及其在量子力学矩阵模型中的出现 引力和超几何函数的推广。 可积系统和逆散射问题发挥着重要作用。 在建立基本 物理学和数学模型用于 描述一下