Semiclassical (zero dispersion limit) solutions to the focusing NLS for a special class of the initial data with both soliton and solitonless cases
Speaker:
Alexander Tovbis, University of Central Florida
Date and Time:
Wednesday, May 19, 2004 - 12:00pm to 12:45pm
Location:
Fields Institute, Room 230
Abstract:
We calculate the leading order term of the solution of the focusing Nonlinear (cubic) Schroedinger Equation (NLS) in the semi-classical limit for a certain one-parameter family of initial conditions. This family contains both solitons and pure radiation. In the pure radiation case, our result is valid for all times t ≥ 0. We utilize the Riemann-Hilbert Problem formulation of the inverse scattering problem to obtain the leading order term of the solution. Error estimates are provided. We also find the long time behavior of semi-classical solutions for solitonless cases within some range of time-small parameter dependence