On small energy solutions of the Nonlinear Schr\"odinger Equation in 1D with a generic trapping potential with a single eigenvalue
Analysis of PDEs
2024-10-01 v1
Abstract
We prove in dimension a result similar to Soffer and Weinstein Jour. Diff. Eq. 98 (1992) capturing for pure power nonlinearities the whole range of exponents . The proof is based on the virial inequality of Kowalczyk \textit{{et al.}} J. Eur. Math. Soc. (JEMS) 24 (2022) with smoothing estimates like in Mizumachi J. Math. Kyoto Univ. 48 (2008).
Keywords
Cite
@article{arxiv.2409.20191,
title = {On small energy solutions of the Nonlinear Schr\"odinger Equation in 1D with a generic trapping potential with a single eigenvalue},
author = {Scipio Cuccagna and Masaya Maeda},
journal= {arXiv preprint arXiv:2409.20191},
year = {2024}
}