Rotating topological edge solitons

TL;DR

This paper investigates how rotation and defocusing nonlinearity influence the formation, stability, and structure of topological edge solitons in waveguide arrays, revealing complex bifurcation behaviors and the emergence of localized states.

Contribution

It introduces the effects of rotation and nonlinearity on topological edge states, demonstrating the formation and stability of rotating topological solitons and their bifurcation structures.

Findings

Rotation modifies the spectrum and edge state positions.

Defocusing nonlinearity restores edge states into the topological gap.

Stable rotating topological solitons and trivial edge states are identified.

Abstract

We address the formation of topological edge solitons in rotating Su-Schrieffer-Heeger waveguide arrays. The linear spectrum of the non-rotating topological array is characterized by the presence of topological gap with two edge states residing in it. Rotation of the array significantly modifies the spectrum and may move these edge states out of the topological gap. Defocusing nonlinearity counteracts this tendency and shifts such modes back into topological gap, where they acquire structure of tails typical for topological edge states. We present rich bifurcation structure for rotating topological solitons and show that they can be stable. Rotation of the topologically trivial array, without edge states in its spectrum, also leads to the appearance of localized edge states, but in a trivial semi-infinite gap. Families of rotating edge solitons bifurcating from the trivial linear edge states exist too and sufficiently strong defocusing nonlinearity can also drive them into the topological gap, qualitatively modifying the structure of their tails.