Final state problem for the cubic nonlinear Schr"odinger equation with repulsive delta potential
Analysis of PDEs
2014-02-27 v2
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.
Cite
@article{arxiv.1402.5185,
title = {Final state problem for the cubic nonlinear Schr"odinger equation with repulsive delta potential},
author = {Jun-ichi Segata},
journal= {arXiv preprint arXiv:1402.5185},
year = {2014}
}
Comments
17pages