Stabilization of single- and multi-peak solitons in the fractional nonlinear Schrödinger equation with a trapping potential
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Publication:2123669
DOI10.1016/J.CHAOS.2020.110222zbMATH Open1495.35199arXiv2008.07866OpenAlexW3081900363MaRDI QIDQ2123669
Author name not available (Why is that?)
Publication date: 14 April 2022
Published in: (Search for Journal in Brave)
Abstract: We address the existence and stability of localized modes in the framework of the fractional nonlinear Schroedinger 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 dipole mode are stabilized by the HO potential at values of the Levy index (the fractionality degree) alpha = 1 and alpha < 1, which lead, respectively, 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.
Full work available at URL: https://arxiv.org/abs/2008.07866
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