Localized Modes in Nonlinear Fractional Systems with Deep Lattices

Xiuye Liu, Boris A. Malomed, Jianhua Zeng

Research output: Contribution to journalArticlepeer-review

Abstract

Solitons in the fractional space, supported by lattice potentials, have recently attracted much interest. The limit of deep 1D and 2D lattices in this system is considered, featuring finite bandgaps separated by nearly flat Bloch bands. Such spectra are also a subject of great interest in current studies. The existence, shapes, and stability of various localized modes, including fundamental gap and vortex solitons, are investigated by means of numerical methods; some results are also obtained with the help of analytical approximations. In particular, the 1D and 2D gap solitons, belonging to the first and second finite bandgaps, are tightly confined around a single cell of the deep lattice. Vortex gap solitons are constructed as four-peak “squares” and “rhombuses” with imprinted winding number (Formula presented.). Stability of the solitons is explored by means of the linearization and verified by direct simulations.

Original languageEnglish
Article number2100482
JournalAdvanced Theory and Simulations
Volume5
Issue number4
DOIs
StatePublished - Apr 2022

Keywords

  • deep lattice
  • fundamental gap and vortex solitons
  • localized modes
  • nonlinear fractional systems

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