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.
