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Systems of solitary-waves in the 1D Gross-Pitaevskii equation, which models atrapped atomic Bose-Einstein condensate, are investigated theoretically. Toanalyse the soliton-like nature of these solitary-waves, a particle analogy forthe solitary-waves is formulated. Exact soliton solutions exist in the absenceof an external trapping potential, which behave in a particle-like manner, andwe find the particle analogy we employ to be a good model also when a harmonictrapping potential is present. In the case of two solitons, the particle modelis integrable, and the dynamics are completely regular. The extension to threeparticles supports chaotic regimes. The agreement between the particle modeland the wave dynamics remains good even in chaotic regimes. In the case of asystem of two solitary waves of equal norm, the solitons are shown to retaintheir phase difference for repeated collisions. This implies that soliton-likeregimes may be found in 3D geometries where solitary waves can be made torepeatedly collide out of phase, stabilising the condensate against collapse.

Bright Solitary-Matter-Wave Collisions in a Harmonic Trap: Regimes of Soliton-like Behaviour