  We consider a two-dimensional (2D) model of a rotating attractive
Bose-Einstein condensate (BEC), trapped in an external potential. First, an
harmonic potential with the critical strength is considered, which generates
quasi-solitons at the lowest Landau level (LLL). We describe a family of the
LLL quasi-solitons using both numerical method and a variational approximation
(VA), which are in good agreement with each other. We demonstrate that kicking
the LLL mode or applying a ramp potential sets it in the Larmor (cyclotron)
motion, that can also be accurately modeled by the VA.
