Stability Theory of Nonlinear Waves

9703695 施特劳斯 该项目的目的是研究波浪的数学模型， 出现在等离子体理论、流体理论和物理学的其他分支中。 科学 将研究稳定性和不稳定性现象，特别是在 带电粒子有无碰撞的动力学理论。 稳定性 问题的各种其他类型的波，包括呼吸，孤立波 和色散波，也将被探讨。 边际能量守恒波 将强调稳定性，并采用数学分析方法， 调查 波以多种形式出现在物理环境中，例如在海洋中， 大气、生化过程、声学、电信等等。 的 最复杂的是非线性的，很难预测 不需要复杂的计算。 其中一些非线性波是 不稳定，这意味着一个小的变化会产生一个大的扰动。 什么浪 哪些是稳定的，哪些是不稳定的，将是这个项目的重点。 基本 理解这些现象的原理是数学的。 这些原则 这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 非线性等离子体波的稳定性与诸如以下的各种应用有关： 核聚变能源研究以及空间卫星和无线电通信。

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.