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Long-time asymptotics for the focusing NLS equation with time-periodic boundary condition

Presented by: 
A Boutet de Monvel [Paris]
Date: 
Wednesday 4th July 2007 - 11:00 to 11:30
Venue: 
INI Seminar Room 1
Abstract: 

We consider the focusing NLS equation on the quarter plane. Initial data are vanishing at infinity while boundary date are time-periodic (ae^[2i\omega t]). The main tool is the asymptotic analysis of the associated matrix Riemann-Hilbert problem. We will show that we obtain 4 different asymptotics in different regions:

region 1: a Zakharov-Manakov vanishing asymptotics region 2: a train of asymptotics solitons region 3: a modulated elliptic wave region 4: a plane wave.

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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons