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} {C}{}erenkov cone when the speed at infinity exceeds the Landau critical speed for the rotons. This yields a {C} {C}{}erenkov-like drag. An analytical approach to the problem is sketched in the weak amplitude limit.
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Pomeau et al. (1993) studied this question.
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