  One dimensional propagation of ultraslow optical pulses in an atomic
Bose-Einstein condensate taking into account the dispersion and the spatial
inhomogeneity is investigated. Analytical and semi-analytical solutions of the
dispersive inhomogeneous wave equation modeling the ultraslow pulse propagation
are developed and compared against the standard wave equation solvers based
upon Cranck-Nicholson and pseudo-spectral methods. The role of curvature of the
trapping potential of the condensate on the amount of dispersion of the
ultraslow pulse is pointed out.
