  When the energy functional of a Bose-condensed state of matter features an
effective gauge potential which depends on the density $\rho$ of the
condensate, the kinetic energy density of the matter field becomes nonlinear in
$\rho$ and additional flow-dependent terms enter the wave equation for the
phase of the condensate wavefunction. To begin with, we consider a certain
class of density-dependent `single-component' gauge potentials, and later
extend this class to encompass more general `multi-component' potentials. The
nonlinear flow terms are cast into the general form of an inner-product between
the velocity field of the fluid and the gauge potential. This is achieved by
introducing a coupling matrix of dimensionless functions $\gamma_{ij}\left(
\rho \right)$, which characterises the particular functional form of the gauge
potential and regulates the strengths of the nonlinear terms accordingly. In
the momentum-transport equation of the fluid, two non-trivial terms emerge due
to the density-dependent vector potential. A body-force of dilation appears as
a product of the gauge potential and the dilation rate of the fluid, while the
fluid stress tensor features a flow-dependent pressure contribution given by
the inner-product of the gauge potential and the current density of the fluid.
This explicit dependence of the fluid pressure on the flow highlights the lack
of Galilean invariance of the nonlinear fluid.
