Model of superflow with rotons

We extend the Gross-Pitaevskii equation for neutral superflows to a model with a roton minimum in the dispersion curve. The flow around an obstacle shows dramatic differences compared to the case without roton minimum: a stationary modulation pattern bifurcates supercritically and transforms continuously into a C Cerenkov cone when the speed at infinity exceeds the Landau critical speed for the rotons. This yields a C Cerenkov-like drag. An analytical approach to the problem is sketched in the weak amplitude limit.