In this paper, by using a compactness method, we study the Cauchy problem of the logarithmic Schrödinger equation with harmonic potential. We then address the existence of ground states solutions as minimizers of the action on the Nehari manifold. Finally, we explicitly compute ground states (Gausson-type solution) and we show their orbital stability
Ardila, A., Cely, L., Squassina, M., Logarithmic Bose-Einstein condensates with harmonic potential, <<ASYMPTOTIC ANALYSIS>>, 2020; (116): 27-40. [doi:10.3233/ASY-191538] [http://hdl.handle.net/10807/154859]
Logarithmic Bose-Einstein condensates with harmonic potential
Squassina, Marco
2020
Abstract
In this paper, by using a compactness method, we study the Cauchy problem of the logarithmic Schrödinger equation with harmonic potential. We then address the existence of ground states solutions as minimizers of the action on the Nehari manifold. Finally, we explicitly compute ground states (Gausson-type solution) and we show their orbital stability
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