Nonuniqueness and nonlinear instability of Gaussons under repulsive harmonic potential
arXiv:2107.10024 · doi:10.1080/03605302.2022.2050257
Abstract
We consider the Schr{ö}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.
arXiv comment14 pages, 3 figures
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