  We analyze the electric current and magnetic field driven domain wall motion
in perpendicularly magnetized ultrathin ferromagnetic films in the presence of
interfacial Dzyaloshinskii-Moriya interaction and both out-of-plane and
in-plane uniaxial anisotropies. We obtain exact analytical Walker-type
solutions in the form of one-dimensional domain walls moving with constant
velocity due to both spin-transfer torques and out-of-plane magnetic field.
These solutions are embedded into a larger family of propagating solutions
found numerically. Within the considered model, we find the dependencies of the
domain wall velocity on the material parameters and demonstrate that adding
in-plane anisotropy may produce domain walls moving with velocities in excess
of 500 m/s in realistic materials under moderate fields and currents.
