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An Isaac Newton Institute Workshop

Effective Computational Methods for Highly Oscillatory Problems: The Interplay between Mathematical Theory and Applications

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

Author: boutet de monvel, anne (Universite Paris7)

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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