The in-plane magnetic field pulse driven domain wall motion on a perpendicularly magnetized nanowire is numerically investigated by performing micromagnetic simulations and magnetic domain wall dynamics are evaluated analytically with one-dimensional collective coordinate models including the interfacial Dzyaloshinskii-Moriya interaction. With the action of the precession torque, the chirality and the magnetic field direction dependent displacements of the magnetic domain walls are clearly observed. In order to move Bloch type and Neel type domain walls, a longitudinal and a transverse in-plane magnetic field pulse are required, respectively. The domain wall type (Bloch or Neel) can easily be determined by the dynamic motion of the domain walls under the applied pulse fields. By applying a temporally asymmetric in-plane field pulse and successive notches in the perpendicularly magnetized nanowire strip line with a proper interval, the concept of racetrack memory based on the synchronous displacements of the chirality dependent multiple domain walls is verified to be feasible. Requirement of multiple domain walls with homogeneous chirality is achieved with the help of Dzyaloshinskii-Moriya interaction.