Spontaneous formation of bright solitons in self-localized impurities in Bose–Einstein condensates

•We use the Time-Dependent-Hartree–Fock–Bogoliubov theory.•Effect of anomalous correlations on bright solitons in Bose-impurity mixtures.•Investigation of bright soliton trains (soliton-molecules) in Bose-impurity mixtures.

We study the formation of bright solitons in the impurity component of Bose–Einstein condensate–impurity mixture by using the time-dependent Hartree–Fock–Bogoliubov theory. While we assume the boson–boson and impurity–boson interactions to be effectively repulsive, their character can be changed spontaneously from repulsive to attractive in the presence of strong anomalous correlations. In such a regime the impurity component becomes a system of effectively attractive atoms leading automatically to the generation of bright solitons. We find that this soliton decays at higher temperatures due to the dissipation induced by the impurity–host and host–host interactions. We show that after a sudden increase of the impurity–boson strength a train of bright solitons is produced and this can be interpreted in terms of the modulational instability of the time-dependent impurity wave function.