  We investigate theoretically the dynamics of a spin-orbit coupled soliton
formed by a self- interacting Bose-Einstein condensate immersed in a random
potential, in the presence of an artificial magnetic field. We find that due to
the anomalous spin-dependent velocity, the synthetic Zeeman coupling can play a
critical role in the soliton dynamics by causing its localization or
delocalization, depending on the coupling strength and on the parameters of the
random potential. The observed effects of the Zeeman coupling qualitatively
depend on the type of self-interaction in the condensate since the spin state
and the self-interaction energy of the condensate are mutually related if the
invariance of the latter with respect to the spin rotation is lifted.
