We study the collective modes of the minority component of a highlyunbalanced Bose-Bose mixtures. In the miscible case the minority componentfeels an effective external potential and we derive an analytical expressionfor the mode frequencies. The latter is independent of the minority componentinteraction strength. In the immiscible case we find that the ground state canbe a two-domain walls soliton. Although the mode frequencies are continuous atthe transition, their behaviour is very different with respect to the misciblecase. The dynamical behaviour of the solitonic structure and the frequencydependence on the inter- and intra-species interaction is numerically studiedusing coupled Gross-Pitaevskii equations.
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