Propagating Ferrodark Solitons in a Superfluid: Exact Solutions and Anomalous Dynamics

Exact propagating topological solitons are found in the easy-plane phase of ferromagnetic spin-1 Bose-Einstein condensates, manifesting themselves as kinks in the transverse magnetization. Propagation is only possible when the symmetry-breaking longitudinal magnetic field is applied. Such solitons have two types: a low energy branch with positive inertial mass and a higher branch solution with negative inertial mass. Both types become identical at the maximum speed, a new speed bound that is different from speed limits set by the elementary excitations. The physical mass, which accounts for the number density dip, is negative for both types. In a finite one-dimensional system subject to a linear potential, the soliton undergoes oscillations caused by transitions between the two types occurring at the maximum speed.