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Nonuniqueness and nonlinear instability of Gaussons under repulsive harmonic potential

Rémi Carles Univ Rennes, CNRS, IRMAR - UMR 6625, Rennes, France Chunmei Su Yau Mathematical Sciences Center, Tsinghua University, Beijing, China

Analysis of PDEs mathscidoc:2205.03005

Communications in Partial Differential Equations, 2022.3
We consider the Schrödinger 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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@inproceedings{rémi2022nonuniqueness,
  title={Nonuniqueness and nonlinear instability of Gaussons under repulsive harmonic potential},
  author={Rémi Carles, and Chunmei Su},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220519160048771049283},
  booktitle={ Communications in Partial Differential Equations},
  year={2022},
}
Rémi Carles, and Chunmei Su. Nonuniqueness and nonlinear instability of Gaussons under repulsive harmonic potential. 2022. In Communications in Partial Differential Equations. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220519160048771049283.
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