Wang Wenlong, Kevrekidis P G
Department of Physics and Astronomy, Texas A&M University, College Station, Texas 77843-4242, USA.
Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USA.
Phys Rev E. 2017 Mar;95(3-1):032201. doi: 10.1103/PhysRevE.95.032201. Epub 2017 Mar 3.
In the present work, we revisit two-component Bose-Einstein condensates in their fully three-dimensional (3D) form. Motivated by earlier studies of dark-bright solitons in the 1D case, we explore the stability of these structures in their fully 3D form in two variants. In one the dark soliton is planar and trapping a planar bright (disk) soliton. In the other case, a dark spherical shell soliton creates an effective potential in which a bright spherical shell of atoms is trapped in the second component. We identify these solutions as numerically exact states (up to a prescribed accuracy) and perform a Bogolyubov-de Gennes linearization analysis that illustrates that both structures can be dynamically stable in suitable intervals of sufficiently low chemical potentials. We corroborate this finding theoretically by analyzing the stability via degenerate perturbation theory near the linear limit of the system. When the solitary waves are found to be unstable, we explore their dynamical evolution via direct numerical simulations which, in turn, reveal wave forms that are more robust. Finally, using the SO(2) symmetry of the model, we produce multi-dark-bright planar or shell solitons involved in pairwise oscillatory motion.
在本工作中，我们重新审视完全三维（3D）形式的双组分玻色 - 爱因斯坦凝聚体。受一维情况下暗 - 亮孤子早期研究的启发，我们以两种变体形式探索这些结构在完全3D形式下的稳定性。在一种变体中，暗孤子是平面的，并捕获一个平面亮（盘状）孤子。在另一种情况下，一个暗球形壳孤子产生一个有效势，在该势中，原子的一个亮球形壳被捕获在第二个组分中。我们将这些解确定为数值精确态（达到规定精度），并进行博戈留波夫 - 德热纳线性化分析，结果表明在足够低化学势的合适区间内，这两种结构都可以是动态稳定的。我们通过在系统线性极限附近利用简并微扰理论分析稳定性，从理论上证实了这一发现。当发现孤立波不稳定时，我们通过直接数值模拟探索它们的动力学演化，这反过来又揭示了更稳健的波形。最后，利用该模型的SO(2)对称性，我们产生了参与成对振荡运动的多暗 - 亮平面或壳孤子。
