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The evolution of soliton trains in dispersion-shiftedfibres (DSFs) in the presence of third-order dispersion (TOD)is investigated. The results show that the collision of neighbouring solitons in the trains can be suppressed by means of a proper TOD, but the maximum transmission distance (or bandwidth) is limited by the increasing soliton separation that results from the TOD. It is also shown that the separation can be suppressed by adjusting the initial phase or amplitude difference between the solitons. These results are helpful to re-establish the potential application of the soliton-based optical-communication systems in DSFs.