Mathematical Sciences: Analytical Aspects of Multidimensional Inverse Scattering

本项目的目标是研究二维空间中的逆散射的解析方面。内容包括：1)确定平面上反散射的最佳函数类，从而使非线性发展方程柯西问题的适定性；2)发展基于逆散射的非线性发展方程的数值算法；3)从一般数据分析孤子的产生和发展；4)非线性双曲型方程的奇性传播。本研究所涉及的方程可应用于流体力学、非线性光学、等离子体物理等领域。

The objective of this project is to study the analytical aspects of inverse scattering in tow spatial dimensions. The topics include: 1) determining the best function classes for inverse scattering on the plane which yield well-posedness for Cauchy problems for nonlinear evolution equations; 2) developing numerical algorithms for nonlinear evolution equations based on inverse scattering; 3) analyzing the emergence and development of solitons from general data; 4) propagation of singularities of nonlinear hyperbolic equations. The equations involved in this research have applications to problems in fluid mechanics, nonlinear optics, plasma physics, etc.