Date: Monday, February 16, 2015
Location: 1866 East Hall (3:00 PM to 4:00 PM)
Title: Direct Scattering for the Benjamin-Ono Equation with Rational Initial Data
Abstract: The Benjamin-Ono (BO) equation describes the weakly nonlinear evolution of one-dimensional interface waves in a dispersive medium. It is an integrable equation, which means that it can be solved using the inverse scattering transform (IST). In practice, this requires knowledge of a Lax pair, which is studied in lieu of the original PDE, to recover the so-called “scattering data”
In this talk, I will briefly introduce the general IST theory for the BO equation. I will then show a construction procedure for the scattering data of the BO equation with a rational initial condition under mild restrictions. The construction procedure uses the analyticity properties of the Lax pair solutions to recover a reflection coefficient, eigenvalues, and phase constants. Lastly, time permitting, I will show that this procedure validates well-known formal asymptotic results in the zero-dispersion limit.
Speaker: Alfredo Wetzel