  Strongly coupled light-matter systems can carry information over long
distances and realize low threshold polariton lasing, condensation and
superfluidity. These systems are highly non-equilibrium in nature, so constant
nonzero fluxes manifest themselves even at the steady-state and are set by a
complicated interplay between nonlinearity, dispersion, pumping, dissipation
and interactions between the various constituents of the system. Based on the
mean-field governing equations of lasers or polariton condensates, we develop a
method for engineering and controlling the velocity profiles by manipulating
the system's spatial pumping and dissipation. We present analytically exact
pumping and dissipation profiles that lead to a large variety of spatially
periodic density and velocity profiles. Besides these, any physically relevant
velocity profiles can be engineered by finding the stationary state of the
conservative nonlinear Schrodinger equation in an external potential related to
the velocity. Our approach opens the way to the controllable implementation of
laser or polariton flows for ultra-fast information processing, integrated
circuits, and analogue simulators.
