  We study numerically the process of vortex nucleation at the wake of a moving
object in superfluids using a generalized and non-local Gross-Pitaevskii model.
The non-local potential is set to reproduce the roton minimum present in the
excitation spectrum of superfluid helium. By applying numerically a
Newton-Raphson method we determine the bifurcation diagram for different types
of non-linearities and object sizes which allow for determining the
corresponding critical velocities. In the case of a non-local potential, we
observe that for small object sizes the critical velocity is simply determined
by the Landau criterion for superfluidity whereas for large objects there is
little difference between all models studied. Finally, we study dynamically in
two and three dimensions how rotons and vortices are excited in the non-local
model of superfluid.
