Korteweg-de Vries Description of Dark Solitons in Bose-Einstein Condensates

We investigate the dynamics of pulses in a cigar-shaped Bose-Einstein condensate with repulsive atom-atom interactions without using Thomas-Fermi approximation. In the linear level our results give the Bogoliubov excitation spectrum for sound propagation with speed c = c₀/√2, where c₀ is the speed for the case without trap. We develop a Korteweg-de Vries (KdV) description for dark soliton propagation in the system and show that it is the quantum pressure that contributes the dispersion necessary for the formation of the dark solitons.