MODEL OF SUPERFLOW WITH ROTONS

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