We study the existence of nontrivial solution curves of the coupled Gross–Pitaevskii equations (CGPEs) in some neighborhoods of bifurcation points. The CGPEs are used as a mathematical model for boson–fermion mixtures (BFM). Linear stability analysis is studied numerically. Three multi-parameter continuation algorithms are proposed for computing the ground states of BFM, where the spectral collocation method is served to discretize the CGPEs. We compare the efficiency of the proposed algorithms with the preconditioned imaginary time evolution method. Extensive numerical results are reported.

中文翻译：

---

玻色子-费米子混合物的连续性和预处理假想时间演化方法

我们研究了分叉点某些邻域中耦合的Gross–Pitaevskii方程（CGPE）的非平凡解曲线的存在。CGPE被用作玻色子-费米子混合物（BFM）的数学模型。对线性稳定性分析进行了数值研究。提出了三种多参数连续算法来计算BFM的基态，其中频谱配比方法用于离散化CGPE。我们将提出的算法与预处理的虚构时间演化方法的效率进行了比较。报告了广泛的数值结果。