Analysis and Applied Mathematics Seminar
Robert Buckingham
University of Cincinnati
Semiclassical dynamics of the three-wave resonant interaction equations
Abstract: The three-wave resonant interaction equations describe the time evolution of the complex amplitudes of three resonant wave modes. We analyze the collision of two or three packets in the semiclassical limit by applying the inverse-scattering transform. Using WKB analysis, we construct an associated semiclassical soliton ensemble, a family of reflectionless solutions intended to accurately approximate the initial data in the semiclassical limit. Plots of the soliton ensembles indicate the space-time plane is partitioned into regions containing either quiescent, slowly varying, or rapidly oscillating waves. This behavior resembles the well-known generation of dispersive shock waves in equations such as the Korteweg-de Vries and nonlinear Schrodinger equations, although the physical mechanism must be different as the system is non-dispersive. This is joint work with Robert Jenkins and Peter Miller.
Monday September 19, 2016 at 4:00 PM in SEO 636