Pairwise Interactions of Ring Dark Solitons with Vortices and other Rings: Stationary States, Stability Features and Nonlinear Dynamics

TL;DR

This study investigates the interactions, stability, and dynamics of ring dark solitons and vortices, revealing that external barrier potentials can stabilize complex multi-ring configurations.

Contribution

It provides a comprehensive analysis of RDS-vortex interactions, stability mechanisms, and the role of external potentials in stabilizing multi-ring systems.

Findings

Vortices partially stabilize RDSs but do not achieve complete stabilization.

External ring-shaped barriers can fully stabilize RDS configurations.

Equilibrium positions of multiple rings depend on curvature and tail interactions.

Abstract

In the present work, we explore analytically and numerically the co-existence and interactions of ring dark solitons (RDSs) with other RDSs, as well as with vortices. The azimuthal instabilities of the rings are explored via the so-called filament method. As a result of their nonlinear interaction, the vortices are found to play a stabilizing role on the rings, yet their effect is not sufficient to offer complete stabilization of RDSs. Nevertheless, complete stabilization of the relevant configuration can be achieved by the presence of external ring-shaped barrier potentials. Interactions of multiple rings are also explored, and their equilibrium positions (as a result of their own curvature and their tail-tail interactions) are identified. In this case too, stabilization is achieved via multi-ring external barrier potentials.