Special UConn Physics Seminar
Shallow Water Waves, Atomic Navigation Sensors, and Inverse Scattering Transform
Department of Physics & Astronomy
University of Southern California
Inverse Scattering Transform is by far the most powerful method of dealing with the long-term behavior of nonlinear systems in hydrodynamics and field theory. Applications include Korteweg-de-Vries equation (KdV) (shallow plane water waves and atmospheric Rossby waves),
Kadomtsev-Petviashvili equation (shallow water waves with slowly varying wavefront), nonlinear Schrodinger equation (NLS) (interacting Bose fields and one-dimensional long-wave-length waves in a deep water), and sine-Gordon equation (differential geometry). I will discuss the KdV and NLS equations in detail. The former constitutes a paradigmatic example of a problem solvable via Inverse Scattering Transform. Despite of the long history of the subject, shallow coastal waves still pose several open problems, such as the mysterious mutual transparency of two two-dimensional solitonic excitations propagating at an angle to each other. The quantum version of the former (NLS) equation is the main tool of atom interferometry, with applications in marine navigation and time keeping.
Thursday, June 17, 2004
Gant Science Complex