Solitons in Quasiperiodic Lattices with Fractional Diffraction

TL;DR

This paper investigates how fractional diffraction influences the formation and stability of solitons in quasiperiodic lattices, providing insights relevant to topological photonics and matter-wave physics.

Contribution

It introduces the study of solitons in quasiperiodic lattices with fractional diffraction using variational and numerical methods, highlighting new stability conditions.

Findings

Stable solitons depend on fractional diffraction parameters.

Fractional diffraction significantly alters soliton properties.

Results have implications for topological photonics and matter-wave dynamics.

Abstract

We study the dynamics of solitons under the action of one-dimensional quasiperiodic lattice potentials, fractional diffraction, and nonlinearity. The formation and stability of the solitons is investigated in the framework of the fractional nonlinear Schr\"odinger equation. By means of variational and numerical methods, we identify conditions under which stable solitons emerge, stressing the effect of the fractional diffraction on soliton properties. The reported findings contribute to the understanding of the soliton behavior in complex media, with implications for topological photonics and matter-wave dynamics in lattice potentials.