Mathematical Sciences: Generation and Propagation of Dispersive Waves in Integrable Systems:

数学科学：可积系统中色散波的产生和传播：

• 批准号: 9103386
• 负责人: Stephanos Venakides
• 金额: $ 5.56万
• 依托单位: Duke University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-08-15 至 1995-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9103386&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Generation; Propagation; Dispersive

This project continues studies in near-integrable systems, concentrating on four main problems: solution of the small-dispersion KdV equation, the Toda shock problem, the small-dispersion long-time limit of the nonlinear Schrodinger equation, and relations of inverse scattering theory to nearly integrable evolution equations. Integrable systems of partial differential equations often have solutions whose properties can be exactly established. This is quite unlike the usual case for nonlinear partial differential equations. What is important here is that often the properties remain when the system is perturbed. Thus one can tell a great deal about otherwise intractable problems. Such problems arise in nonlinear optics (for example, in the design of long-distance communication networks using fiber optics), in the motion of waves in nonlinear acoustic media, and in flows around thin wings.

该项目继续研究近可积系统， 集中讨论四个主要问题： 小色散KdV方程，户田激波问题， 非线性薛定谔的小色散长时间极限 方程，以及逆散射理论与近 可积发展方程部分可积系统 微分方程的解的性质通常 准确地建立。 这与通常的情况不同， 非线性偏微分方程 重要的 这就是，当系统被 心烦意乱 因此，人们可以说很多关于 否则会出现棘手的问题。 这样的问题出现在非线性光学中（例如， 远程通信网络的设计 纤维光学），在非线性声学中的波的运动 介质和薄翼周围的气流。