Stability Theory of Nonlinear Waves

非线性波的稳定性理论

• 批准号: 9703695
• 负责人: Walter Strauss
• 金额: $ 12.19万
• 依托单位: Brown University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-07-15 至 2001-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9703695&HistoricalAwards=false
• 关键词: Stability; Theory; Nonlinear; Waves

9703695 Strauss The purpose of this project is to study mathematical models of waves that occur in the theories of plasmas, of fluids, and of other branches of physical science. Stability and instability phenomena will be investigated, particularly in the kinetic theory of charged particles with and without collisions. Stability problems for a variety of other kinds of waves, including breathers, solitary waves and dispersive waves, will also be explored. Energy conserving waves of marginal stability will be emphasized, and methods of mathematical analysis will be employed in the investigations. Waves occur in many forms in the physical environment, such as in the ocean, the atmosphere, biochemical processes, acoustics, telecommunications, and so on. The most complicated ones are the nonlinear ones, where it is difficult to predict the outcomes without very complex calculations. Some of these nonlinear waves are unstable, which means that a small change creates a large disturbance. Which waves are stable and which are unstable will be the focus of this project. The basic principles for understanding these phenomena are mathematical. These principles are fundamental to the creation of high-performance computing algorithms. We shall investigate the stability theory especially within the theory of physical plasmas. The stability of nonlinear plasma waves is relevant to such diverse applications as fusion energy research and satellite and radio communications in space.

9703695 Strauss 该项目的目的是研究等离子体、流体和物理科学其他分支理论中出现的波的数学模型。 将研究稳定性和不稳定现象，特别是在有碰撞和没有碰撞的带电粒子的动力学理论中。 还将探讨各种其他类型的波的稳定性问题，包括呼吸波、孤立波和色散波。 将强调边际稳定的能量守恒波，并采用数学分析方法进行研究。 波在物理环境中以多种形式出现，例如在海洋、大气、生化过程、声学、电信等中。 最复杂的是非线性问题，如果没有非常复杂的计算就很难预测结果。 其中一些非线性波是不稳定的，这意味着微小的变化会产生很大的干扰。 哪些波浪是稳定的，哪些波浪是不稳定的将是该项目的重点。 理解这些现象的基本原理是数学原理。 这些原则是创建高性能计算算法的基础。 我们将研究稳定性理论，特别是在物理等离子体理论中。 非线性等离子体波的稳定性与聚变能研究以及太空卫星和无线电通信等多种应用相关。