Pairwise interactions of ring dark solitons with vortices and other rings: Stationary states, stability features, and nonlinear dynamics
Wenlong Wang, Théodore Kolokolnikov, D. J. Frantzeskakis, R. Carretero-González, P. G. Kevrekidis
Abstract
In the present work, we explore analytically and numerically the coexistence 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, the external trap, and their tail-tail interactions) are identified. In this case too, stabilization is achieved via multiring external barrier potentials.