Dynamics of ring dark solitons in Bose-Einstein condensates and nonlinear optics

TL;DR

This paper develops an analytical framework for understanding the dynamics of ring dark solitons in Bose-Einstein condensates and nonlinear optics, validated by numerical simulations.

Contribution

It introduces a quasiparticle approach to derive effective equations of motion for ring dark solitons applicable to various nonlinear media.

Findings

Analytical equations match numerical simulations closely.

Energy conservation law governs ring dark soliton dynamics.

Applicable to both optical and condensate systems.

Abstract

Quasiparticle approach to dynamics of dark solitons is applied to the case of ring solitons. It is shown that the energy conservation law provides the effective equations of motion of ring dark solitons for general form of the nonlinear term in the generalized nonlinear Schroedinger or Gross-Pitaevskii equation. Analytical theory is illustrated by examples of dynamics of ring solitons in light beams propagating through a photorefractive medium and in non-uniform condensates confined in axially symmetric traps. Analytical results agree very well with the results of our numerical simulations.