  We consider one-dimensional mixtures of an atomic Bose-Einstein condensate
(BEC) and Tonks- Giradeau (TG) gas. The mixture is modeled by a coupled system
of the Gross-Pitaevskii equation for the BEC and the quintic nonlinear
Schroedinger equation for the TG component. An immiscibility condition for the
binary system is derived in a general form. Under this condition, three types
of BEC-TG interfaces are considered: domain walls (DWs) separating the two
components; bubble-drops (BDs), in the form of a drop of one component immersed
into the other (BDs may be considered as bound states of two DWs); and bound
states of bright and dark solitons (BDSs). The same model applies to the
copropagation of two optical waves in a colloidal medium. The results are
obtained by means of systematic numerical analysis, in combination with
analytical Thomas-Fermi approximations (TFAs). Using both methods, families of
DW states are produced in a generic form. BD complexes exist solely in the form
of a TG drop embedded into the BEC background. On the contrary, BDSs exist as
bound states of TG bright and BEC dark components, and vice versa.

Quantum Gases;Pattern Formation and Solitons;Optics