Nonuniqueness and nonlinear instability of Gaussons under repulsive harmonic potential
Analysis of PDEs
2023-12-04 v1 Mathematical Physics
math.MP
Abstract
We consider the Schr{\"o}dinger equation with a nondispersive logarithmic nonlinearity and a repulsive harmonic potential. For a suitable range of the coefficients, there exist two positive stationary solutions, each one generating a continuous family of solitary waves. These solutions are Gaussian, and turn out to be orbitally unstable. We also discuss the notion of ground state in this setting: for any natural definition, the set of ground states is empty.
Keywords
Cite
@article{arxiv.2107.10024,
title = {Nonuniqueness and nonlinear instability of Gaussons under repulsive harmonic potential},
author = {Rémi Carles and Chunmei Su},
journal= {arXiv preprint arXiv:2107.10024},
year = {2023}
}
Comments
14 pages, 3 figures