Nonuniqueness and nonlinear instability of Gaussons under repulsive harmonic potential
Nonuniqueness and nonlinear instability of Gaussons under repulsive harmonic potential
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 …