The Whitham Equations and Their Solutions

惠瑟姆方程及其解

• 批准号: 0103849
• 负责人: Fei-Ran Tian
• 金额: --
• 依托单位: Ohio State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-07-15 至 2004-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0103849&HistoricalAwards=false
• 关键词: Whitham; Equations; Their; Solutions

NSF Award Abstract - DMS-0103849Mathematical Sciences: The Whitham Equations and Their SolutionsAbstractDMS-0103849TianThe Principal Investigator will consider a variety of problems concerning the Whitham equations, which describe the macrostructure of nonlinear dispersive oscillations. In particular, the Principal Investigator will study (1) multiphase Whitham equations in one spatial dimension, and (2) Whitham equations in several spatial dimensions. The primary interest of the first project is in the interaction of single-phase oscillations and generation and propagation of double and higher phase oscillations. The basic goal of the second project is to understand how the zero phase Whitham solution develops singularities in several dimensional space. The proposed methods will be both analytical and computational. Results of this project will have broad impact in interdisciplinary work. The multiphase Whitham equations in one spatial variable play an essential role in both zero dispersion limit and modulation theories of nonlinear dispersive oscillations. They also have applications in the transmission of pulses in optical fibers. The Whitham equations in several spatial dimensions are intrinsically connected to Landau-Ginzburg models in topological field theory and the Seiberg-Witten solution in supersymmetric Yang-Mills Theory.

NSF奖摘要-DMS-0103849数学科学：Whitham方程及其解DMS-0103849天首席研究员将考虑与Whitham方程有关的各种问题，这些方程描述了非线性色散振荡的宏观结构。特别是，首席调查员将研究(1)一个空间维度的多相Whitham方程，以及(2)几个空间维度的Whitham方程。第一个项目的主要兴趣在于单相振荡和双相及更高相振荡的产生和传播之间的相互作用。第二个项目的基本目标是了解零相位Whitham解是如何在多维空间中发展奇点的。建议的方法将是解析和计算的。该项目的成果将对跨学科工作产生广泛影响。一个空间变量的多相Whitham方程在非线性色散振荡的零色散极限理论和调制理论中都起着至关重要的作用。它们在光纤中传输脉冲方面也有应用。多维的Whitham方程与拓扑场论中的Landau-Ginzburg模型和超对称Yang-Mills理论中的Seiberg-Witten解有着内在的联系。