Recently, a novel bifurcation technique known as deflated continuation was applied to the single-component nonlinear Schrödinger (NLS) equation with a parabolic trap in two spatial dimensions. This bifurcation analysis revealed previously unknown solutions, shedding light on this fundamental problem in the physics of ultracold atoms. In the present work, we take this a step further by applying deflated continuation to two coupled NLS equations, which – feature a considerably more complex landscape of solutions. Upon identifying branches of solutions, we construct the relevant bifurcation diagrams and perform spectral stability analysis to identify parametric regimes of stability and instability and to understand the mechanisms by which these branches emerge. The method reveals a remarkable wealth of solutions. These include both well-known states arising from the Cartesian and polar small amplitude limits of the underlying linear problem, but also a significant number of more complex states that arise through (typically pitchfork) bifurcations.

最近，一种被称为放气连续的新型分叉技术被应用于二维空间上具有抛物线形陷阱的单分量非线性薛定ding（NLS）方程。这种分叉分析揭示了以前未知的解决方案，从而阐明了超冷原子物理学中的这一基本问题。在当前的工作中，我们通过对两个耦合的NLS方程应用紧缩的延续来进一步迈出这一步，这些方程具有更复杂的解决方案。确定解决方案的分支后，我们构建相关的分歧图并进行光谱稳定性分析，以识别稳定性和不稳定性的参数范围，并了解这些分支出现的机制。该方法揭示了非凡的解决方案。