Logarithmic Bose–Einstein condensates with harmonic potential

Article type: Research Article

Authors: Ardila, Alex H.^a | Cely, Liliana^b | Squassina, Marco^{c; **; *}

Affiliations: [a] Instituto Nacional de Matemática Pura e Aplicada – IMPA, Estrada Dona Castorina, 110 CEP 22460-320, Rio de Janeiro, RJ, Brasil. E-mail: ardila@impa.br | [b] Instituto de Matemática e Estatística, Departamento de Matemática, Universidade de São Paulo, 05508-090, São Paulo, SP, Brazil. E-mail: mlcelyp@ime.usp.br | [c] Dipartimento di Matematica e Fisica, Università Cattolica del Sacro Cuore, Via dei Musei 41, I-25121 Brescia, Italy. E-mail: marco.squassina@unicatt.it

Correspondence: [*] Corresponding author. E-mail: marco.squassina@unicatt.it.

Note: [**] Member of Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA).

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.

Keywords: Logarithmic Schrödinger equation, harmonic potential, stability

DOI: 10.3233/ASY-191538

Journal: Asymptotic Analysis, vol. 116, no. 1, pp. 27-40, 2020