Mathematical Sciences: Nonlinear Wave Motion

数学科学：非线性波动

• 批准号: 9304390
• 负责人: Harvey Segur
• 金额: $ 6万
• 依托单位: University of Colorado at Boulder
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-06-15 至 1997-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9304390&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Nonlinear; Wave; Motion

This research encompasses three separate lines of study: a) Asymptotics beyond all orders; b) Kinetic theory and resonant triads, and c) Models for motion of curves and surfaces in space. The results have potential for important applications in nonlinear dynamics and applications of the KAM theory. The KAM theorem asserts that under appropriate circumstances most of the trajectories of the system remain regular at the onset of chaos; only a few trajectories actually become irregular, or chaotic. So far there is no available theory that can identify which trajectories become chaotic under small perturbations. If successful, the work proposed here will enable scientists to work with dynamical systems containing both chaotic and regular trajectories. This issue is important in many fields, one of which is the design of plasma fusion devices like tokomaks.

这项研究涵盖三个独立的研究领域：a) 超越所有阶的渐近学； b) 动力学理论和共振三元组，以及 c) 空间曲线和曲面运动模型。 该结果在非线性动力学和 KAM 理论的应用中具有重要应用潜力。 KAM 定理断言，在适当的情况下，系统的大多数轨迹在混沌开始时仍然保持规则； 只有少数轨迹实际上变得不规则或混乱。 到目前为止，还没有可用的理论可以识别哪些轨迹在小扰动下变得混乱。 如果成功，这里提出的工作将使科学家能够研究包含混沌和规则轨迹的动力系统。 这个问题在许多领域都很重要，其中之一就是托科马克等等离子体聚变装置的设计。