On small energy solutions of the Nonlinear Schr\"odinger Equation in 1D with a generic trapping potential with a single eigenvalue

Scipio Cuccagna; Masaya Maeda

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arXiv · 2409.20191

On small energy solutions of the Nonlinear Schr\"odinger Equation in 1D with a generic trapping potential with a single eigenvalue

Scipio Cuccagna·Masaya Maeda

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Abstract

We prove in dimension $d=1$ a result similar to Soffer and Weinstein Jour. Diff. Eq. 98 (1992) capturing for pure power nonlinearities the whole range of exponents $p>1$. 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).

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Scipio Cuccagna, Masaya Maeda. 2024-09-30. On small energy solutions of the Nonlinear Schr\"odinger Equation in 1D with a generic trapping potential with a single eigenvalue. https://arxiv.org/abs/2409.20191

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