玻色-爱因斯坦凝聚（BEC）在凝聚态物理、量子信息和量子计算等领域具有广泛应用。而孤子由于其在传输过程中能够保持原有的形状进行稳定地传输而在非线性科学中占有较重要地位。而BEC的发现为孤子的研究提供了一个良好的平台。但是，目前BEC中的孤子研究主要依赖于实验分析和数值计算，缺乏相应的解析研究，在全面分析问题上还存在欠缺。本项目将通过BEC的量子统计力学分析，运用“自旋相干态平均法”，建立三维BEC动力学方程，并利用相关数学方法得到方程的孤子解，分析孤子不同条件下的动力学行为。最后，对所建立的模型添加微扰，研究BEC中孤子相互作用及孤子在BEC体系中稳定存在条件，并对所建模型进行修正，保证BEC中孤子相干演化的稳定性。

Bose Einstein condensation (BEC) is widely used in condensed matter physics, quantum information and quantum computation. Solitons can be used in the nonlinear science because of its stable transmission in the transmission process. The discovery of BEC provides a good platform for the study of solitons. However, the research of solitons in BEC mainly depends on the experimental analysis and numerical calculation, and there is a lack of corresponding analytic researches. In this project, we will use the "spin coherent state average method" to establish the three-dimensional BEC dynamic equation by BEC quantum statistical mechanics analysis. The soliton solutions of the equation are obtained by using the mathematical method, and the dynamic behavior of solitons under different conditions is analyzed. Finally, the perturbation of the model is established to study the soliton interaction in the BEC and the stable condition of solitons in the BEC system, and the model is modified to guarantee the stability of the soliton coherent evolution in BEC.