# Nonlinear Waves in an Experimentally Motivated Ring-shaped Bose-Einstein Condensate Setup

## TL;DR

This paper constructs and analyzes various stationary soliton states in a ring-shaped Bose-Einstein condensate, exploring their stability, dynamics, and experimental creation methods within a nonlinear Schrödinger framework.

## Contribution

It systematically identifies and characterizes a wide range of soliton and vortex states in a ring-shaped BEC using bifurcation analysis and stability studies.

## Key findings

- Multiple stable and unstable soliton configurations identified.
- Unstable states can lead to persistent vortical dynamics.
- Phase-imprinting can create these states in experiments.

## Abstract

We systematically construct stationary soliton states in a one-component, two-dimensional, repulsive, Gross-Pitaevskii equation with a ring-shaped target-like trap similar to the potential used to confine a Bose-Einstein condensate in a recent experiment [Eckel, et al.\ {\em Nature} {\bf 506}, 200 (2014)]. In addition to the ground state configuration, we identify a wide variety of excited states involving phase jumps (and associated dark solitons) inside the ring. These configurations are obtained from a systematic bifurcation analysis starting from the linear, small atom density, limit. We study the stability, and when unstable, the dynamics of the most basic configurations. Often these lead to vortical dynamics inside the ring persisting over long time scales in our numerical experiments. To illustrate the relevance of the identified states, we showcase how such dark-soliton configurations (even the unstable ones) can be created in laboratory condensates by using phase-imprinting techniques.