Recent experimental observations of spin–orbit coupling (SOC) in Bose–Einstein condensates (BECs) open the way for investigating novel physics of nonlinear waves with promising applications in atomic physics and condensed matter physics. The interplay between atomic interactions and SOC are crucial for the understanding of the dynamics of nonlinear waves in BECs with SOC. Here, in the small linear coupling regime, an approach is presented which allows us to derive an infinite number of novel approximate solutions of the Gross–Pitaevskii equations (GPEs) in one and two dimensions including SOCs, time-dependent external potentials, and nonlinearities leading to breathers and periodic as well as quasiperiodic nonlinear waves. To verify the theoretical predictions we perform numerical simulations which show for several cases a very good agreement with the analytics. For the case of one spatial dimension, it is shown that functions describing the external potential and nonlinearities cannot be chosen independently. The management of the solutions is clarified along with some important physical properties such as Josephson oscillations and Rosen–Zener oscillations.

最近对玻色-爱因斯坦凝聚体 (BEC) 中自旋轨道耦合 (SOC) 的实验观察为研究非线性波的新物理学开辟了道路，在原子物理学和凝聚态物理学中具有广阔的应用前景。原子相互作用和 SOC 之间的相互作用对于理解具有 SOC 的 BEC 中非线性波的动力学至关重要。在这里，在小线性耦合机制中，提出了一种方法，该方法使我们能够在一维和二维中推导出无限数量的 Gross-Pitaevskii 方程 (GPE) 的新近似解，包括 SOC、时间相关的外部电位和非线性导致呼吸和周期性以及准周期性非线性波。为了验证理论预测，我们进行了数值模拟，这表明在几种情况下与分析非常吻合。对于一维空间的情况，表明不能独立选择描述外部电位和非线性的函数。解决方案的管理与一些重要的物理特性一起得到澄清，例如约瑟夫森振荡和罗森-齐纳振荡。