Matter-wave interference mechanisms in one-dimensional Bose-Einstein condensates that allow for the controlled generation of dark soliton trains upon choosing suitable box-type initial configurations are described. First, the direct scattering problem for the defocusing nonlinear Schrödinger equation with nonzero boundary conditions and general box-type initial configurations is discussed, and expressions for the discrete spectrum corresponding to the dark soliton excitations generated by the dynamics are obtained. It is found that the size of the initial box directly affects the number, size and velocity of the solitons, while the initial phase determines the parity of the solutions. The analytical results obtained for the untrapped system are compared to those of numerical simulations of the Gross-Pitaevskii equation, both in the absence and in the presence of a harmonic trap. The numerical results bear out the analytical results with excellent agreement.

中文翻译：

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玻色-爱因斯坦冷凝物中按需生成暗孤子列

描述了在一维玻色-爱因斯坦凝聚物中的物质波干扰机制，该机制允许在选择合适的箱型初始配置后控制暗孤子序列的产生。首先，讨论了具有非零边界条件和一般盒型初始构型的散焦非线性薛定ding方程的直接散射问题，并获得了由动力学产生的暗孤子激发对应的离散谱的表达式。发现初始盒的大小直接影响孤子的数量，大小和速度，而初始阶段决定了溶液的奇偶性。将未陷井系统获得的分析结果与Gross-Pitaevskii方程的数值模拟进行了比较，无论是否存在谐波陷阱，都可以。数值结果与分析结果吻合得很好。