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arXiv · 2008.07866

Stabilization of single- and multi-peak solitons in the fractional nonlinear Schroedinger equation with a trapping potential

Yunli Qiu·Boris A. Malomed·Dumitru Mihalache·Xing Zhu·Xi Peng·Yingji He
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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.

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Yunli Qiu, Boris A. Malomed, Dumitru Mihalache, Xing Zhu, Xi Peng, Yingji He. 2020-08-18. Stabilization of single- and multi-peak solitons in the fractional nonlinear Schroedinger equation with a trapping potential. https://arxiv.org/abs/2008.07866

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