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

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

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Article number110222
JournalChaos, Solitons and Fractals
Volume140
DOIs
StatePublished - Nov 2020

Keywords

  • Fractional nonlinear Schrödinger equation
  • Harmonic-oscillator potential
  • Lévy index
  • Soliton

Fingerprint

Dive into the research topics of 'Stabilization of single- and multi-peak solitons in the fractional nonlinear Schrödinger equation with a trapping potential'. Together they form a unique fingerprint.

Cite this