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01/21/03 Colloquium
DR. ALEXANDER TOVBIS
Department of Mathematics
University of Central Florida
Department of Mathematics
University of Central Florida
Semi-classical Solutions for the Focusing Nonlinear Schroedinger Equation
Abstract: We discuss the semi-classical limit of the focusing Nonlinear (cubic) Schroedinger Equations (NLS) for a certain one-parameter family of initial conditions, which contains both soliton and pure radiation cases. Starting with the explicit scattering data, obtained in my previous work (with S. Venakides), we apply the method of Riemann-Hilbert Problem (RHP) to find the leading order term of the solution through the technique of inverse scattering. This is a joint work with S. Venakides and X. Zhou.