@article{d2a62be6a66f4c979e77f8d8bedd4120,
title = "Orbital stability and uniqueness of the ground state for the non-linear schr{\"o}dinger equation in dimension one",
abstract = "We prove that standing-waves which are solutions to the non-linear Schr{\"o}dinger equation in dimension one, and whose profiles can be obtained as minima of the energy over the mass, are orbitally stable and non-degenerate, provided the non-linear term satisfies a Euler differential inequality. When the non-linear term is a combined pure power-type, then there is only one positive, symmetric minimum of prescribed mass.",
keywords = "Schr{\"o}dinger, Stability, uniqueness",
author = "Daniele Garrisi and Vladimir Georgiev",
note = "Funding Information: 2010 Mathematics Subject Classification. Primary: 35Q55; Secondary: 47J35. Key words and phrases. Stability, uniqueness, Schr{\"o}dinger. The first author was supported by INHA UNIVERSITY Research Grant through the project number 51747-01 titled “Stability in non-linear evolution equations”. The second author was supported by University of Pisa, project no. PRA-2016-41 “Fenomeni singolari in problemi de-terministici e stocastici ed applicazioni”; by INDAM, GNAMPA - Gruppo Nazionale per l{\textquoteright}Analisi Matematica, la Probabilit{\`a} e le loro Applicazioni and by Institute of Mathematics and Informatics, Bulgarian Academy of Sciences and Top Global University Project, Waseda University. ∗ Corresponding author: Daniele Garrisi.",
year = "2017",
month = aug,
doi = "10.3934/dcds.2017184",
language = "English",
volume = "37",
pages = "4309--4328",
journal = "Discrete and Continuous Dynamical Systems- Series A",
issn = "1078-0947",
publisher = "Southwest Missouri State University",
number = "8",
}