@article{8ea3d203c750420d8dca81d1c8f3382a,
title = "Final State Problem for the Cubic Nonlinear Schr{\"o}dinger Equation with Repulsive Delta Potential",
abstract = "We consider the asymptotic behavior in time of solutions to the cubic nonlinear Schr{\"o}dinger equation with repulsive delta potential (δ-NLS). We shall prove that for a given small asymptotic profile u ap, there exists a solution u to (δ-NLS) which converges to u apin L 2(ℝ) as t → ∞. To show this result we exploit the distorted Fourier transform associated to the Schr{\"o}dinger equation with delta potential.",
keywords = "Asymptotic behavior, Schr{\"o}dinger equation with delta potential",
author = "Segata, {Jun Ichi}",
note = "Funding Information: The author is partially supported by MEXT, Grant-in-Aid for Young Scientists (A) 25707004 and Grant for the Sumitomo Foundation, Basic Science Research Projects 120043. Publisher Copyright: {\textcopyright} 2015, Taylor & Francis Group, LLC.",
year = "2015",
month = feb,
day = "1",
doi = "10.1080/03605302.2014.930753",
language = "English",
volume = "40",
pages = "309--328",
journal = "Communications in Partial Differential Equations",
issn = "0360-5302",
publisher = "Taylor and Francis Ltd.",
number = "2",
}