Bright Matter-Wave Soliton Collisions in a Harmonic Trap: Regular and   Chaotic Dynamics
  Collisions between bright solitary waves in the 1D Gross-Pitaevskii equation with a harmonic potential, which models a trapped atomic Bose-Einstein condensate, are investigated theoretically. A particle analogy for the solitary waves is formulated, which is shown to be integrable for a two-particle system. The extension to three particles is shown to support chaotic regimes. Good agreement is found between the particle model and simulations of the full wave dynamics, suggesting that the dynamics can be described in terms of solitons both in regular and chaotic regimes, thus presenting a paradigm for chaos in wave-mechanics. 
A. D. Martin, C. S. Adams and S. A. Gardiner