Modified scattering for the $1d$ cubic NLS with a repulsive delta potential

Published 1 Aug 2017 in math.AP | (1708.00392v2)

Abstract: We consider the initial-value problem for the $1d$ cubic nonlinear Schr\"odinger equation with a repulsive delta potential. We prove that small initial data in a weighted Sobolev space lead to global solutions that decay in $L^\infty$ and exhibit modified scattering.

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