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

preprint2017arXivOpen access

We consider the initial-value problem for the $1d$ cubic nonlinear Schrödinger 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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Modified scattering for the $1d$ cubic NLS with a repulsive delta potential

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Modified scattering for the 1d1d1d cubic NLS with a repulsive delta potential

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