On a Fractional Schrödinger equation in the presence of Harmonic potential
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2019
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| _version_ | 1866910860140609536 |
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| author | Ding, Zhiyan Hajaiej, Hichem |
| author_facet | Ding, Zhiyan Hajaiej, Hichem |
| contents | 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. Our results explain the effect of each term of the Schrödinger equation : The fractional power, the power of the nonlinearity and the harmonic potential. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1908_05719 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | On a Fractional Schrödinger equation in the presence of Harmonic potential Ding, Zhiyan Hajaiej, Hichem Analysis of PDEs 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. Our results explain the effect of each term of the Schrödinger equation : The fractional power, the power of the nonlinearity and the harmonic potential. |
| title | On a Fractional Schrödinger equation in the presence of Harmonic potential |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/1908.05719 |