Solitary waves on vortex lines in Ginzburg--Landau models

TL;DR

This paper numerically investigates axisymmetric solitary waves along vortex lines in Bose-Einstein condensates, revealing their properties, formation via bubble collapse, and resulting wave trains, advancing understanding of vortex dynamics in quantum fluids.

Contribution

It introduces a numerical method to find solitary waves on vortex lines in Bose-Einstein condensates and details their formation through bubble collapse, a novel insight into vortex dynamics.

Findings

A continuous family of solitary waves is identified in the momentum-energy plane.

Collapse of a bubble on a vortex line generates solitary waves and wave trains.

Vortex core compression occurs during collapse, leading to wave formation.

Abstract

Axisymmetric disturbances that preserve their form as they move along the vortex lines in uniform Bose-Einstein condensates are obtained numerically by the solution of the Gross-Pitaevskii equation. A continuous family of such solitary waves is shown in the momentum ($p$) -- substitution energy ($\hat{\cal E}$) plane with $p\to 0.09 \rho \kappa^3/c^2, \hat{\cal E}\to 0.091 \rho \kappa^3/c$ as $U \to c$, where $\rho$ is the density, $c$ is the speed of sound, $\kappa$ is the quantum of circulation and $U$ is the solitary wave velocity. It is shown that collapse of a bubble captured by a vortex line leads to the generation of such solitary waves in condensates. The various stages of collapse are elucidated. In particularly, it is shown that during collapse the vortex core becomes significantly compressed and after collapse two solitary wave trains moving in opposite directions are formed on the vortex line.