gap soliton states (or arrays of gap solitons) can also be formed. This is shown in Fig. \[fig3\]c for the case of a two hump BEC condensate obtained as inter-site symmetric (IS) gap-soliton (notice that the state is symmetric around a maxima instead than a minima of the periodic potential). We see that also in this case the fermionic density increases in correspondence with the two bosonic humps and two fermionic levels are formed in the corresponding effective potential (see Fig. \[fig3\]d). We have checked that both the OS and the IS modes are very stable under time evolution (see Fig. \[fig4\]).

Gap- solitons with different symmetries with respect to the OL, such onsite-asymmetric (OA) and intersite-asymmetric (IA), can also exist in BFM but they appear to be metastable under time evolution. In Fig. \[fig5\]a we show a gap-soliton of type IA together with two fermionic states trapped in the condensate. In panel (b) of this figure we depict the time evolution of the bosonic and fermionic densities of the IA gap-soliton as obtained from direct numerical integration of Eqs. (\[bose-fermi-eqns\]).

![[**(a)**]{} Wavefunction of the intersite-asymmetric (IA) gap-soliton (thick line) plotted together with the wavefunctions of the lowest and first 