Open AccessOn a fractional Schrödinger equation in the presence of harmonic potential
Author(s) -
Zhiyan Ding,
Hichem Hajaiej
Publication year - 2021
Publication title -
electronic research archive
Language(s) - English
Resource type - Journals
ISSN - 2688-1594
DOI - 10.3934/era.2021047
Subject(s) - mathematics , schrödinger equation , harmonic , mathematical physics , stability (learning theory) , type (biology) , mathematical analysis , physics , quantum mechanics , computer science , machine learning , ecology , biology
In this paper, we establish the existence of ground state solutions for a fractional Schrödinger equation in the presence of a harmonic trapping potential. We also address the orbital stability of standing waves. Additionally, we provide interesting numerical results about the dynamics and compare them with other types of Schrödinger equations [ 11 , 18 ]. Our results explain the effect of each term of the Schrödinger equation: the fractional power, the power of the nonlinearity, and the harmonic potential.