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.

中文翻译：

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具有二体和三体相互作用的玻色-爱因斯坦凝聚中的干涉和孤子

用辛方法在一维上对谐波俘获势中的玻色-爱因斯坦凝聚进行了数值研究。检验了不变量的守恒性，并给出了不同非线性系数的特征值。研究了具有吸引力的二体相互作用和排斥性的三体相互作用的凝聚体，并讨论了凝聚体在自由空间和谐波俘获势中的干涉和孤子行为。结果表明，具有吸引力的二体相互作用的凝聚物的动力学行为与具有排斥性的二体相互作用的凝聚物的动力学行为有很大不同，并且排斥性三体相互作用的加入对状态的稳定性和动力学行为具有显着影响系统的。