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We consider the asymptotic behavior in time of solutions to the cubicnonlinear Schr"odinger equation with repulsive delta potential (delta-NLS). Weshall prove that for a given asymptotic profile, there exists a solution to(delta-NLS) which converges to the given asymptotic profile as time goesinfinity. To show this result we exploit the distorted Fourier transformassociated to the Schr"odinger equation with delta potential.

Final state problem for the cubic nonlinear Schr"odinger equation with repulsive delta potential