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On a fractional Schrödinger equation in the presence of harmonic potential

  • Received: 01 November 2020 Revised: 01 March 2021 Published: 24 June 2021
  • Primary: 35Q55; Secondary: 47J30, 35J60

  • 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.

    Citation: Zhiyan Ding, Hichem Hajaiej. On a fractional Schrödinger equation in the presence of harmonic potential[J]. Electronic Research Archive, 2021, 29(5): 3449-3469. doi: 10.3934/era.2021047

    Related Papers:

  • 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.



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