Localized matter-waves patterns with attractive interaction in rotating potentials

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.