In this work, we explore systematically various SO(2)-rotation-induced multiple dark–dark (DD) soliton breathing patterns obtained from stationary and spectrally stable multiple dark–bright (DB) and DD waveforms in trapped one-dimensional, two-component atomic Bose–Einstein condensates. The stationary states stemming from the associated linear limits (as the eigenfunctions of the quantum harmonic oscillator problem) are parametrically continued to the nonlinear regimes by varying the respective chemical potentials, i.e. from the low-density linear limits to the high-density Thomas–Fermi (TF) regimes. We perform a Bogolyubov–de Gennes spectral stability analysis to identify stable parametric regimes of these states, finding a wide range of stability intervals in the TF regimes for all of the states considered herein. Upon applying an SO(2)-rotation to stable steady states, one-, two-, three-, four-, and many DD soliton breathing patterns are observed in the numerical simulations. Furthermore, analytic solutions up to three DB solitons in the homogeneous setting, and three-component systems are also investigated.

在这项工作中，我们系统地探索了各种 SO(2) 旋转诱导的多重暗-暗 (DD) 孤子呼吸模式，这些模式从静止和光谱稳定的多重暗-亮 (DB) 和 DD 波形中获得组分原子玻色-爱因斯坦凝聚。源自相关线性极限（作为量子谐振子问题的本征函数）的稳态通过改变各自的化学势，即从低密度线性极限到高密度 Thomas-Fermi，参数化地延续到非线性状态(TF) 制度。我们执行 Bogolyubov-de Gennes 谱稳定性分析来识别这些状态的稳定参数状态，找到本文考虑的所有状态的 TF 状态中的大范围稳定区间。在将 SO(2) 旋转应用于稳定的稳态后，在数值模拟中观察到一、二、三、四和许多 DD 孤子呼吸模式。此外，还研究了均匀设置中多达三个 DB 孤子的解析解，以及三分量系统。