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。本课题旨在研究非线性色散哈密顿系统的孤立波解的稳定性。他对分析Korteweg- de Vries方程中临界孤子的不稳定性以及离散峰和呼吸的稳定性特别感兴趣。另一个主题是非线性狄拉克方程中孤波的轨道稳定性。这里使用的工具包括离散估计和正态分析。他还计划研究无限维哈密顿系统中的吸引子理论，特别是确定这种系统何时具有有限维吸引子。要研究的方程出现在海洋动力学、大气和量子场论中。他们的分析将有助于理解从最小的电子产品和芯片到大的天气模式等尺度上的相关物理现象。

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.