  We consider a Bose-Einstein condensate with repulsive interactions confined
in a 1D ring where a Dirac delta is rotating at constant speed. The spectrum of
stationary solutions in the delta comoving frame is analyzed in terms of the
nonlinear coupling, delta velocity, and delta strength, which may take positive
and negative values. It is organized into a set of energy levels conforming a
multiple swallowtail structure in parameter space, consisting in bright
solitons, gray and dark solitonic trains, and vortices. Analytical expressions
in terms Jacobi elliptic functions are provided for the wave functions and
chemical potentials. We compute the critical velocities and perform a
Bogoliubov analysis for the ground state and first few excited levels,
establishing possible adiabatic transitions between the stationary and stable
solutions. A set of adiabatic cycles is proposed in which gray solitons and
vortices of arbitrary quantized angular momenta are obtained from the ground
state by setting and unsetting a rotating delta.
