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When the energy functional of a Bose-condensed state of matter features aneffective gauge potential which depends on the density $\rho$ of thecondensate, the kinetic energy density of the matter field becomes nonlinear in$\rho$ and additional flow-dependent terms enter the wave equation for thephase of the condensate wavefunction. To begin with, we consider a certainclass of density-dependent `single-component' gauge potentials, and laterextend this class to encompass more general `multi-component' potentials. Thenonlinear flow terms are cast into the general form of an inner-product betweenthe velocity field of the fluid and the gauge potential. This is achieved byintroducing a coupling matrix of dimensionless functions $\gamma_{ij}\left(\rho \right)$, which characterises the particular functional form of the gaugepotential and regulates the strengths of the nonlinear terms accordingly. Inthe momentum-transport equation of the fluid, two non-trivial terms emerge dueto the density-dependent vector potential. A body-force of dilation appears asa product of the gauge potential and the dilation rate of the fluid, while thefluid stress tensor features a flow-dependent pressure contribution given bythe 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 lackof Galilean invariance of the nonlinear fluid.

On the hydrodynamics of Bose-condensed fluids subject to density-dependent gauge potentials