Nonlinear Dispersive Hamiltonian Systems: Solitary Waves and Global Attractors

非线性色散哈密顿系统：孤立波和全局吸引子

• 批准号: 0600863
• 负责人: Andrew Comech
• 金额: --
• 依托单位: Texas A&M Research Foundation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-06-01 至 2010-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0600863&HistoricalAwards=false
• 关键词: Nonlinear; Dispersive; Hamiltonian; Systems; Solitary

Nonlinear Dispersive Hamiltonian Systems: Solitary Wavesand Global Attractors.Abstract of Proposed ResearchAndrew Comech This project is to study the stability of solitary wave solutions of nonlinear dispersive Hamiltonian systems. He is particularly interested in analyzing the instability of the critical solitons in the Korteweg- de Vries equation and the stability of discrete peakons and breathers. Another topic is the orbital stability of solitary waves in the nonlinear Dirac equations. Tools to be used here include dispersive estimates and normal form analysis. He also plans to investigate the theory of attractors in infinite dimensional Hamiltonian systems and, in particular, to determine when such systems have finite dimensional attractors. The equations to be studied appear in ocean dynamics, in the atmosphere and in quantum field theories. Their analysis will help understand associated physical phenomena on scales ranging from the very smallest electronics and chips to large weather patterns.

非线性分散性哈密顿系统：孤立的波和全球吸引子。提议的研究和comech的吸收是为了研究非线性分散性汉密尔顿系统孤立波解决方案的稳定性。他特别感兴趣地分析Kortewegde Vries方程中关键孤子的不稳定性以及离散的Peachons和呼吸器的稳定性。另一个主题是非线性狄拉克方程中孤立波的轨道稳定性。此处要使用的工具包括分散估计和正常形式分析。他还计划研究无限尺寸哈密顿系统中吸引子的理论，尤其是确定何时具有有限的维度吸引子。要研究的方程式出现在海洋动力学，大气和量子场理论中。他们的分析将有助于了解从最小的电子和芯片到大天气模式等尺度上相关的物理现象。