Mathematical Sciences: Development and Applications of Periodic Soliton Theory for Nearly Integrable P.D.E.

数学科学：近可积偏微分方程的周期孤子理论的发展和应用

• 批准号: 8803465
• 负责人: M Forest
• 金额: $ 7.09万
• 依托单位: Ohio State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-06-01 至 1991-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8803465&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Development; Applications; Periodic

This project focuses on the investigation of mathematical models of nonlinear wave phenomena such as the appearance and persistence of large eddies and the onset of turbulence in fluid flow. The formation and oscillation of coherent structures are phenomena which such as the Kuramoto-Sivashinisky, Sine-Gordon and Nonlinear Schroedinger equations. By employing methods of inverse spectral theory, invariant manifold theory and numerical methods, this project will be aimed at explaining the common mechanism which gives rise to the above phenomena in these disparate models.

该项目的重点是调查数学 非线性波现象的模型，如外观和 流体中大涡的持续性和湍流的开始 流 相干结构的形成和振荡是 如Kuramoto-Sivashinisky，Sine-Gordon等现象 非线性薛定谔方程 通过采用 逆谱理论、不变流形理论和数值方法 方法，该项目将旨在解释共同的 导致上述现象的机制 不同的模型。