| Abstract: |
| We consider the initial value problem for the cubic nonlinear Schr\{o}dinger equation (NLS) with a repulsive delta potential in one space dimension. Our goal is to describe the long-time decay and asymptotics of small solutions to (NLS). From the linear scattering theory, we expect that (NLS) will not scatter to the solution to the linear equation. We prove that if the initial data is sufficiently small in a weighted Sobolev space, then there exists a unique global solution to (NLS) that decays in $L^{\infty}$ and exhibits modified scattering. |
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