Mathematical Sciences: Analytical Aspects of Multidimensional Inverse Scattering

本项目的目标是研究分析方面的问题， 在两个空间维度上的逆散射。 的主题 包括：1）确定最佳函数类， 在平面上的散射产生柯西适定性 非线性发展方程问题; 2）发展 非线性发展方程的数值算法 逆散射; 3）分析了 一般数据的孤子; 4） 非线性双曲型方程 本研究中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

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.