Logarithmic Bose-Einstein condensates with harmonic potential

2018/01/02 by Alex H. Ardila, Ardila, Alex H., Liliana Cely +3 · 1 citation
Mathematics · #35Q40 #35Q55 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35Q40 #msc:35Q55

paper · pdf · doi:10.48550/arxiv.1801.01382

12 pages, updated version

arxiv created 2019/02/08 · arxiv updated 2019/02/11

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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