  We investigate certain invariance properties of quantum fluids subject to a
nonlinear gauge potential. In particular, we derive the covariant
transformation laws for the nonlinear potentials under a space-time Galilean
boost and consider U(1) gauge transformations. We find that the hydrodynamic
canonical field equations are form-invariant in the case of external gauge
functions, but not for nonlinear gauge functionals. Hence, nonlinear gauge
potentials are non-trivial potentials which may not be "gauged-away". Notably,
for a 1D superfluid, attempting to do so generates the gauge-pressure of the
fluid in the Hamiltonian density. Further, we investigate how the field
equations transform under arbitrary Galilean transformations. We find that the
immediate lack of Galilean covariance is restored under a suitably chosen
transformation rule set for the potentials, which is identical in form to that
of a Schr\"odinger particle coupled to external scalar and vector potentials.
