Profiles of the solitary waves that accompany moving vertical Bloch lines in domain walls in ferrite garnets have been numerically calculated using the two-dimensional Slonczewski equations. In the in-plane magnetic field (i.e., the field in the plane of the sample), which is of the order of the demagnetization field and perpendicular to the domain wall plane, vertical Bloch lines are stationary. In weak planar fields, the dynamics of vertical Bloch lines is significantly affected by the motion of horizontal Bloch lines. This leads to decay of a vertical Bloch line with a topological charge of Nit to a packet of N separate lines with charges of 7T (7r-lines). The velocity of separate ir-lines of the packet is approximately equal to that of a solitary vertical Bloch line with charge it in one dimension. The velocity of the packet as a whole is lower than that of a vertical Bloch line with charge Nit in one dimension because of the continual annihilation of leading lines and creation of trailing lines in the packet. Experiments in in-plane magnetic fields have confirmed the calculations. Stable solitary waves with narrow leading fronts, which accompany vertical Bloch lines, are generated at low domain-wall velocities in the absence of in-plane magnetic fields, and at high domain-wall velocities when they are present. This fact allowed the success of earlier measurements of dynamics and soliton-like behavior of vertical Bloch lines in collisions. In the presence of a sufficiently high in-plane magnetic field, one can use the one-dimensional Slonczewski equations to interpret measurements of motion and collisions of vertical Bloch lines in an in-plane magnetic field.
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