Bogoliubov Quasiparticles Carried by Dark Solitonic Excitations in Nonuniform Bose-Einstein Condensates

We consider the noncondensate part of the Bose gas in presence of dark solitons. We get a stationary equation of Bogoliubov quasiparticles and find that these Bogoliubov quasiparticles are confined by a dark soliton and carried to propagate with it. This model of the compound structure of the soliton and Bogoliubov quasiparticles provides more precise description of localized sound excitations in Bose-Einstein condensates.