Condition for convective instability of dark solitons

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.

► Conditions for absolute or convective instability of dark solitons are derived.
► Velocity of expansion of instability front equals to the minimal group velocity.
► Growth rate of length of dark solitons generated by the flow is estimated.