Mathematical Sciences: Analysis of Solitary Wave Phenomena

本项目将专注于孤立波现象的分析。文中将讨论孤立波分析中的几个相关问题，包括孤立波的存在性、唯一性和稳定性。此外，还将考虑各种近似方程的有效性和非线性偏微分方程组或积分-微分方程组的某些严格性质。非线性分析工具将得到一些数值模拟和逆散射理论的特殊方法的补充。要研究的系统出现在许多非线性科学领域，包括流体力学、非线性光学、固体物理、海洋学和气象学。

This project shall concentrate on the analysis of solitary wave phenomena. Several related questions in the analysis of solitary waves will be examined, including their existence, uniqueness and stability. In addition, the validity of various approximate equations and certain rigorous properties of nonlinear dispersive systems of partial differential or integro- differential equations will be considered. The tools of nonlinear analysis will be supplemented by some numerical simulation and the special methods of inverse scattering theory. The systems to be studied arise in many areas of nonlinear science including fluid mechanics, nonlinear optics, solid state physics, oceanography and meteorology.