The domain wall motion of field-driven transverse domain walls in biaxial ferromagnets is investigated by solving the Landau-Lifshitz-Gilbert equation. It is demonstrated that with increasing easy-plane or hard-axis anisotropy D-h different types of domain wall motion occur. The different scenarios correspond to different velocity equations. In the limit of absent hard-axis anisotropy (D-h/J = 0) a precessional domain wall motion can be found while for D-h/J not equal 0 a steady domain wall motion interrupted by a Walker breakdown at high fields prevails. In the limit of huge anisotropies (D-h/J >> 0) a domain wall motion damped by emission of spin waves occurs. The connection between magnetic systems and the theory of solitons is discussed.