Mathematical Sciences: Waves in Nonlinear Dispersive and Hyperbolic Systems

数学科学：非线性色散和双曲系统中的波

• 批准号: 9008520
• 负责人: Rodolfo Rosales
• 金额: $ 19.5万
• 依托单位: Massachusetts Institute of Technology
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-06-15 至 1993-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9008520&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Waves; Nonlinear; Dispersive

The principal investigator will continue his important studies of three major areas of nonlinear wave theory: nonlinear dispersive waves, focussing of weak shock waves at caustics and catastrophic instabilities in square-wave detonations. The methods of study involve the use of analytic and asymptotic techniques supplemented with numerical analysis. Such a combined approach is called for because the phenomena under study occur at the boundaries of existing theories. Many phenomena in nature cannot be described adequately with linear models; nature is inherently "nonlinear". The proposed research involves the study of wave motions that are described by nonlinear differential equations. A good example is the "breaking" of an ocean wave as it approaches the beach. In order to describe the behavior of such a nonlinear wave the principal investigator will use asymptotic analysis in concert with numerical analysis to obtain qualitative and quantitative information.

首席研究员将继续他的重要研究， 非线性波动理论的三个主要领域：非线性色散 弱冲击波聚焦焦散线和灾难性 方波爆炸的不稳定性 学习方法 涉及分析和渐近技术的使用 并辅以数值分析。 这样一种综合办法 之所以需要，是因为所研究的现象发生在 现有理论的边界。 自然界中的许多现象 用线性模型充分描述;自然是固有的 “非线性”。 拟议的研究涉及波的研究 由非线性微分方程描述的运动。 一个很好的例子是“打破”的海浪，因为它 接近海滩。 为了描述这种行为， 一个非线性波，首席研究员将使用渐近 分析与数值分析相结合，以获得定性 和定量信息。