  A domain wall and spin supercurrent can coexist in magnets with easy-cone
anisotropy owing to simultaneous spontaneous breaking of Z$_2$ and U(1)
symmetries. Their interaction is theoretically investigated in quasi
one-dimensional ferromagnets within the Landau-Lifshitz-Gilbert phenomenology.
Specifically, we show that spin supercurrent can exert the torque on a domain
wall and thereby drive it. We also show, as a reciprocal phenomenon, a
field-induced motion of a domain wall can generate spin supercurrent.
