Talk Abstract:

Riemann Hilbert Approach to Whitham Modulation Equations, and the Description of Oscillations in Semiclassical Focusing Nonlinear Schroedinger

Ken T.R. McLaughlin
University of Arizona

Recent developments in the study of singular limits of integrable systems has yielded some new insights regarding the complete integrability of associated Whitham modulation equations. We consider several examples, including the semi-classical limit of the focusing NLS equation, and derive explicit solution formulae for the associated modulation equations, for general classes of initial data. This work allows us to provide a rather detailed description of the onset and evolution of oscillations in the amplitude of the solution of the focusing nonlinear Schroedinger equation in the semi-classical limit. This is joint work with Peter Miller (Monash University, Australia) and Spyros Kamvissis (Univ. of Patras, Greece).

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