Dynamics of localized waves in quasi-one-dimensional imbalanced binary Bose-Einstein condensates

In the framework of coupled Gross-Pitaevskii equations, we explore the dynamics of localized waves in quasi-1D imbalanced binary Bose-Einstein condensates where the intra-component interaction is repulsive, while the inter-component one is attractive. The existence regimes of stable self-trapped localized states in the form of symbiotic solitons have been analyzed. Imbalanced mixtures, where the number of atoms in one component exceeds the number of atoms in the other component, are considered in parabolic potential and box-like trap. A variational approach has been developed which allows us to find the stationary state of the system and frequency of small amplitude oscillations near the equilibrium. It is shown that the strength of inter-component coupling can be retrieved from the frequency of the localized state's vibrations. When all the intra-species and inter-species interactions are repulsive, we numerically find a new type of symbiotic solitons resembling dark-bright solitons. The motion of the minority component in the surrounding gas of the majority component with different velocities reveals its superfluid properties.