Solitary waves of Bose-Einstein condensed atoms confined in finite rings

TL;DR

This paper investigates solitary wave solutions in Bose-Einstein condensates confined in finite ring geometries, revealing how wave properties change with ring size and boundary conditions.

Contribution

It provides a detailed analysis of solitary waves in finite rings, extending understanding from infinite to finite geometries with boundary effects.

Findings

Density profile approximates infinite ring when ring is large

Wave velocity saturates as ring size approaches wave size

Density and velocity cannot vanish simultaneously in finite rings

Abstract

Motivated by recent progress in trapping Bose-Einstein condensed atoms in toroidal potentials, we examine solitary-wave solutions of the nonlinear Schr\"odinger equation subject to periodic boundary conditions. When the circumference of the ring is much larger than the size of the wave, the density profile is well approximated by that of an infinite ring, however the density and the velocity of propagation cannot vanish simultaneously. When the size of the ring becomes comparable to the size of the wave, the density variation becomes sinusoidal and the velocity of propagation saturates to a constant value.