Landau dynamics of a grey soliton in a trapped condensate

TL;DR

This paper models the motion of grey solitons in a trapped condensate as Landau dynamics of quasi-particles, demonstrating that they behave like particles with mass 2m and move without changing shape.

Contribution

It introduces a quasi-particle model for grey soliton dynamics in a trap, aligning with perturbation theory and extending to vortex rings.

Findings

Grey solitons behave as particles with mass 2m.

Soliton density profiles remain undeformed during motion.

The model is consistent with perturbation theory for dark solitons.

Abstract

It is shown that grey soliton dynamics in an one-dimensional trap can be treated as Landau dynamics of a quasi-particle. A soliton of arbitrary amplitude moves in the trapping potential without deformation of its density profile as a particle of mass $2m$. The dynamics in the local density approximation is shown to be consistent with the perturbation theory for dark solitons. Dynamics of a vortex ring in a trap is discussed qualitatively.