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: 8702625
• 负责人: Rodolfo Rosales
• 金额: $ 10.71万
• 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: 1987
• 资助国家: 美国
• 起止时间: 1987-06-15 至 1991-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8702625&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Waves; Nonlinear; Dispersive

This ongoing research program on nonlinear waves will focus on the following three topics: 1. Functional path integrals. 2. Exact modulation. 3. Three wave resonant interactions. The first two topics are concerned with the study of some relationships among equations with the Painleve property, equations solvable by the Inverse Scattering Transform method, the theory of wave modulation and representation of solution of partial differential equations by path integrals. The last topic is concerned with the study of weakly nonlinear interactions of waves in strictly hyperbolic systems. The mathematical theory of nonlinear waves is a mathema- tical model of physical wave propagation. The conclusions deduced from the theory are generally useful to our under- standing of many natural and technological phenomena. The present research program on nonlinear waves is aimed toward a better understanding of resonance and instability which are causes for failures in structural and fluid systems. The research results are expected to contribute to better designs for many such engineereing systems.

这项正在进行的非线性波研究计划将 重点关注以下三个主题： 1.泛函路径积分。 2.精确调制。 3.三波共振相互作用。 前两个主题是关于研究一些 具有Painleve性质的方程之间的关系， 可解的逆散射变换方法，理论的 波调制与解的表示 用路径积分求解偏微分方程的 最后一个主题是关于弱非线性的研究。 严格双曲系统中的波的相互作用。 非线性波的数学理论是一个复杂的理论， 物理波传播的理论模型。 的结论 从理论上推导出来的一般是有用的，我们的下- 许多自然现象和技术现象。 本 非线性波的研究计划旨在 更好地理解共振和不稳定性， 是结构和流体系统故障的原因。 的 研究结果有望有助于更好的设计 对于许多这样的工程系统来说。