  The shape and dynamics of the nonrelativistic gauge vortex string in the
parity-broken media is considered, upon reducing the problem to finding the
extremum of the Abelian Higgs model effective action with the fixed B-type
helicity of the gauge field. It is shown that in contrast with the case of the
fixed A-type helicity, the static solution of the Ginzburg-Landau energy
functional in the London limit is the helix with the specific relation between
the curvature and torsion of the vortex line depending on the strength of the
space parity violating contribution of the Lifshitz invariant. A nonlinear
dynamical equation is linearized in case of small oscillations around the
helical contour, and the polarization and dispersion law of the propagated
waves are obtained.
