Abstract
We prove that standing-waves which are solutions to the non-linear Schrödinger 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.
Original language | English |
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Pages (from-to) | 4309-4328 |
Number of pages | 20 |
Journal | Discrete and Continuous Dynamical Systems |
Volume | 37 |
Issue number | 8 |
DOIs | |
Publication status | Published - Aug 2017 |
Externally published | Yes |
Keywords
- Schrödinger
- Stability
- uniqueness
ASJC Scopus subject areas
- Analysis
- Discrete Mathematics and Combinatorics
- Applied Mathematics
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Garrisi, D., & Georgiev, V. (2017). Orbital stability and uniqueness of the ground state for the non-linear schrödinger equation in dimension one. Discrete and Continuous Dynamical Systems, 37(8), 4309-4328. https://doi.org/10.3934/dcds.2017184