Nonlinear Problems in Fluid Dynamics and Inverse Scattering
Mark J. Ablowitz, Gregory Beylkin, D. Sather · 1993
The inverse scattering of a class of differential-difference equations and multidimensional operators has been constructed. Solutions of nonlinear wave equations arising in fluid dynamics and plasma physics were found and analyzed. Novel and fast computational algorithms were developed and in relevant nonlinear problems wavelet bases with controlled localization properties in the time-frequency domain have proven to be an effective tool. Landau type amplitude equations governing the small gap Taylor problem have been obtained and analyzed. Detailed project summaries and research activities are given in the attached document. A list of published papers, preprints, and invited lectures are included