Mathematical Sciences: Analysis of Solitary Waves and Multi-Solitons

数学科学：孤波和多孤子分析

• 批准号: 9310612
• 负责人: Robert Sachs
• 金额: $ 5.73万
• 依托单位: George Mason University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-07-15 至 1997-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9310612&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Analysis; Solitary; Waves

This project will involve the analysis of solitary waves, multi- solitons, and related phenomena in the theory of nonlinear dispersive systems without dissipation. Several questions in the analysis of solitary waves will be examined, including their existence, uniqueness, and stability. Numerical investigations will supplement theoretical analysis. In addition, the validity of various approximate equations and certain rigorous properties of nonlinear dispersive systems of partial differential or integro-differential equations will be considered. The tools of nonlinear analysis will be supplemented by some numerical simulation and the special methods of inverse scattering theory. Solitary waves are localized, nonlinear, progressing waves that subsist on a balance struck between nonlinear and dispersive effects. They arise in many physical settings. Rigorous analysis is often quite difficult since the problem is nonlinear from the outset. Nonlinear model equations have been developed that predict the presence of solitary waves and capture their qualitative features. The systems to be studied arise in many areas of nonlinear science including fluid mechanics, nonlinear optics, solid state physics, oceanography, and meteorology.

本计画将涉及无耗散非线性色散系统理论中孤立波、多孤立子及相关现象之分析。 孤波分析中的几个问题将被研究，包括它们的存在性、唯一性和稳定性。 数值研究将补充理论分析。 此外，各种近似方程的有效性和某些严格的性质的非线性色散系统的偏微分或积分微分方程将被考虑。 非线性分析的工具将通过一些数值模拟和逆散射理论的特殊方法来补充。 孤立波是局部的、非线性的、渐进的波，其存在于非线性和色散效应之间的平衡。 它们出现在许多物理环境中。 严格的分析往往是相当困难的，因为问题从一开始就是非线性的。 非线性模型方程已经开发，预测孤立波的存在，并捕捉其定性特征。 要研究的系统出现在非线性科学的许多领域，包括流体力学，非线性光学，固态物理，海洋学和气象学。