Topological defects such as magnetic solitons, vortices, Bloch lines, and skyrmions have started to play an important role in modern magnetism because of their extraordinary stability, which can be exploited in the production of memory devices. Recently, a novel type of antisymmetric exchange interaction, namely the Dzyaloshinskii-Moriya interaction (DMI), has been uncovered and found to influence the formation of topological defects. Exploring how the DMI affects the dynamics of topological defects is therefore an important task. Here we investigate the dynamic domain wall (DW) under a strong DMI and find that the DMI induces an annihilation of topological vertical Bloch lines (VBLs) by lifting the four-fold degeneracy of the VBL. As a result, velocity reduction originating from the Walker breakdown is completely suppressed, leading to a soliton-like constant velocity of the DW. Furthermore, the strength of the DMI, which is the key factor for soliton-like DW motion, can be quantified without any side effects possibly arising from current-induced torques or extrinsic pinnings in magnetic films. Our results therefore shed light on the physics of dynamic topological defects, which paves the way for future work in topology-based memory applications.