  Stationary waves in a superfluid magnetoexciton gas in nu = 1 quantum Hall
bilayers are considered. The waves are induced by counter-propagating
electrical currents that flow in a system with a point obstacle. It is shown
that stationary waves can emerge only in imbalanced bilayers in a certain
diapason of currents. It is found that the stationary wave pattern is modified
qualitatively under a variation of the ratio of the interlayer distance to the
magnetic length d/l. The advantages of use graphene-dielectric-graphene
sandwiches for the observation of stationary waves are discussed. We determine
the range of parameters (the dielectric constant of the layer that separates
two graphene layers and the ratio d/l) for which the state with superfluid
magnetoexcitons can be realized in such sandwiches. Typical stationary wave
patterns are presented as density plots
