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arXiv · 2107.10024

Nonuniqueness and nonlinear instability of Gaussons under repulsive harmonic potential

Rémi Carles·Chunmei Su
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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.

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Rémi Carles, Chunmei Su. 2021-07-21. Nonuniqueness and nonlinear instability of Gaussons under repulsive harmonic potential. https://doi.org/10.1080/03605302.2022.2050257

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