  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.
