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arXiv · 1402.5185

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

Jun-ichi Segata
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Abstract

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

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Jun-ichi Segata. 2014-02-21. Final state problem for the cubic nonlinear Schr"odinger equation with repulsive delta potential. https://arxiv.org/abs/1402.5185

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