Abstract
The Bose–Einstein condensates in a harmonic trapping potential are studied numerically in one dimension by the symplectic method. The conservations of invariants are tested and the eigenvalues of different nonlinear coefficients are presented. Condensates with attractive two-body interaction and repulsive three-body interaction are investigated, and the interference and soliton behaviors of the condensates are discussed both in free space and in a harmonic trapping potential. It is demonstrated that the dynamic behaviors of condensates with attractive two-body interaction are quite different to those with repulsive two-body interactions, and the addition of a repulsive three-body interaction has significant effect on the stability of the state and the dynamical behavior of the system.
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