×

Logarithmic Bose-Einstein condensates with harmonic potential. (English) Zbl 1442.35413

Summary: 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.

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
35Q41 Time-dependent Schrödinger equations and Dirac equations
82C10 Quantum dynamics and nonequilibrium statistical mechanics (general)
35A15 Variational methods applied to PDEs
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness
35C08 Soliton solutions
PDFBibTeX XMLCite
Full Text: DOI arXiv