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Nonuniqueness and nonlinear instability of Gaussons under repulsive harmonic potential

Abstract : 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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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-03293209
Contributor : Rémi Carles Connect in order to contact the contributor
Submitted on : Tuesday, July 20, 2021 - 6:02:59 PM
Last modification on : Tuesday, October 19, 2021 - 10:48:09 AM
Long-term archiving on: : Thursday, October 21, 2021 - 7:03:53 PM

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  • HAL Id : hal-03293209, version 1
  • ARXIV : 2107.10024

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Rémi Carles, Chunmei Su. Nonuniqueness and nonlinear instability of Gaussons under repulsive harmonic potential. 2021. ⟨hal-03293209⟩

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