Condition for convective instability of dark solitons

TL;DR

This paper derives the condition for the transition from absolute to convective instability in dark solitons, showing that unstable wave packets expand at the minimal group velocity, with implications for Bose-Einstein condensate flows.

Contribution

It provides a simple analytical derivation of the convective instability condition for dark solitons, supported by numerical simulations.

Findings

Unstable wave packets expand at the minimal group velocity.

The growth rate of dark solitons in BEC flow is estimated.

Analytical results are confirmed by numerical simulations.

Abstract

Simple derivation of the condition for the transition point from absolute instability of plane dark solitons to their convective instability is suggested. It is shown that unstable wave packet expands with velocity equal to the minimal group velocity of the disturbance waves propagating along a dark soliton. The growth rate of the length of dark solitons generated by the flow of Bose-Einstein condensate past an obstacle is estimated. Analytical theory is confirmed by the results of numerical simulations.