Gap solitons in quasiperiodic optical lattices

TL;DR

This paper constructs and analyzes stable and unstable solitons in 1D and 2D quasiperiodic optical lattices described by Gross-Pitaevskii equations, revealing their mobility, collisions, and transformation behaviors.

Contribution

It introduces new families of stable and unstable solitons in 1D and 2D quasiperiodic lattices, including explicit solutions and stability analysis.

Findings

Stable 1D solitons exist in three bandgaps.

Tightly bound 1D solitons are found in strong potentials, with some transforming into breathers.

Stable fundamental and vortical solitons are identified in the 2D model.

Abstract

Families of solitons in one- and two-dimensional (1D and 2D) Gross-Pitaevskii equations with the repulsive nonlinearity and a potential of the quasicrystallic type are constructed (in the 2D case, the potential corresponds to a five-fold optical lattice). Stable 1D solitons in the weak potential are explicitly found in three bandgaps. These solitons are mobile, and they collide elastically. Many species of tightly bound 1D solitons are found in the strong potential, both stable and unstable (unstable ones transform themselves into asymmetric breathers). In the 2D model, families of both fundamental and vortical solitons are found and are shown to be stable.