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Nonuniqueness and nonlinear instability of Gaussons under repulsive harmonic potential

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 Added by Remi Carles
 Publication date 2021
  fields Physics
and research's language is English




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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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