Quantum Phases of Attractive Matter Waves in a Toroidal Trap
  Investigating the quantum phase transition in a ring from a uniform attractive Bose-Einstein condensate to a localized bright soliton we find that the soliton undergoes transverse collapse at a critical interaction strength, which depends on the ring dimensions. In addition, we predict the existence of other soliton configurations with many peaks, showing that they have a limited stability domain. Finally, we show that the phase diagram displays several new features when the toroidal trap is set in rotation. 
A. Parola, L. Salasnich, R. Rota, and L. Reatto