  In the presence of a linear potential with an arbitrary time-dependence,
Hirota method is developed carefully for applying into the effective mean-field
model of quasi-one-dimensional Bose-Einstein condensation with repulsive
interaction. We obtain the exact nonautonomous soliton solution (NSS)
analytically. These solutions show that the time-dependent potential can affect
the velocity of NSS. In some special cases the velocity has the character of
both increase and oscillation with time. A detail analysis for the asymptotic
behaviour of solutions shows that the collision of two NSSs is elastic.
