Stationary waves in a superfluid gas of electron-hole pairs in bilayers

Stationary waves in the condensate of electron-hole pairs $n\ensuremath{-}p$ bilayer system are studied. The demonstrates transition from a uniform (superfluid) to nonuniform (supersolid) state. precursor this is appearance roton-type minimum collective mode spectrum. occur flow past an obstacle. It shown that manifests itself rather complicated stationary wave pattern, with several families crests which cross one another. found pattern essentially modified under variation density and velocity. formed main part by short-wave modes case point contribution long-wave clearly visible weak extended obstacle, where resembles ship pattern.