 Stabilization of single- and multi-peak solitons in the fractional nonlinear Schrödinger equation with a trapping potentialYunli Qiu, Boris A. Malomed, Dumitru Mihalache, Xing Zhu, Xi Peng and Yingji He Chaos, Solitons & Fractals, 2020, vol. 140, issue C Abstract: We address the existence and stability of localized modes in the framework of the fractional nonlinear Schrödinger equation (FNSE) with the focusing cubic or focusing-defocusing cubic-quintic nonlinearity and a confining harmonic-oscillator (HO) potential. Approximate analytical solutions are obtained in the form of Hermite-Gauss modes. The linear stability analysis and direct simulations reveal that, under the action of the cubic self-focusing, the single-peak ground state and the dipole mode are stabilized by the HO potential at values of the Lévy index (the fractionality degree) α ≤ 1, which lead to the critical or supercritical collapse in free space. In addition to that, the inclusion of the quintic self-defocusing provides stabilization of higher-order modes, with the number of local peaks up to seven, at least. Keywords: Fractional nonlinear Schrödinger equation; Lévy index; Soliton; Harmonic-oscillator potential (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:140:y:2020:i:c:s0960077920306184 DOI: 10.1016/j.chaos.2020.110222 Access Statistics for this article Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros More articles in Chaos, Solitons & Fractals from Elsevier |
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