  We demonstrate that rotating quasi-one-dimensional potentials, periodic or
parabolic, support solitons in settings where they are otherwise impossible.
Ground-state and vortex solitons are found in defocusing media, if the rotation
frequency exceeds a critical value. The revolving periodic potentials exhibit
the strongest stabilization capacity at a finite optimum value of their
strength, while the rotating parabolic trap features a very sharp transition to
stability with the increase of rotation frequency.
