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.
|Number of pages||20|
|Journal||Discrete and Continuous Dynamical Systems- Series A|
|Publication status||Published - 2017 Aug 1|
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Applied Mathematics