We analyse the effects of bandwidth limited amplification on the multiple collisions between optical solitons of two 10 Gbit/s different wavelength multiplexed channels in a fiber transmission system with lumped amplifiers. We find that the soliton arrival time jitter at the system output which is due to the accumulated frequency shifts resulting from asymmetric collisions in the periodically amplified fiber link may be strongly damped by filtering, as it occurs for the case of the Gordon-Haus effect.