Continuation and preconditioned imaginary time evolution methods for boson–fermion mixtures

Abstract

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.