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Self-localization of a small number of Bose particles in a superfluid Fermi system

We consider self-localization of a small number of Bose particles immersed in a large homogeneous superfluid mixture of fermions in three and one dimensional spaces. Bosons distort the density of surrounding fermions and create a potential well where they can form a bound state analogous to a small polaron state. In the three dimensional volume we observe the self-localization for repulsive interactions between bosons and fermions. In the one dimensional case bosons self-localize as well as for attractive interactions forming, together with a pair of fermions at the bottom of the Fermi sea, a vector soliton. We analyze also thermal effects and show that small non-zero temperature affects the pairing function of the Fermi-subsystem and has little influence on the self-localization phenomena.