Localized modes in arrays of boson-fermion mixtures

It is shown that the mean-field description of a boson-fermion mixture with a dominating fermionic component, loaded in a one-dimensional optical lattice, is reduced to the nonlinear Schroedinger equation with a periodic potential and periodic nonlinearity. In such a system there exist localized modes having peculiar properties. In particular, for some regions of parameters there exists a lower bound for a number of bosons necessary for creation of a mode, while for other domains small amplitude gap solitons are not available in the vicinity of either of the gap edges. We found that the lowest branch of the symmetric solution either does not exist or exists only for a restricted range of energies in a gap, unlike in pure bosonic condensates. The simplest bifurcations of the modes are shown and stability of the modes is verified numerically