On a fractional Schrödinger equation in the presence of harmonic potential

Abstract

<p style='text-indent:20px;'>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 [<xref ref-type="bibr" rid="b11">11</xref>,<xref ref-type="bibr" rid="b18">18</xref>]. Our results explain the effect of each term of the Schrödinger equation: the fractional power, the power of the nonlinearity, and the harmonic potential.</p>