  In this paper we study a system of coupled nonlinear Schrodinger equations
modelling a quantum degenerate mixture of bosons and fermions. We analyze the
stability of plane waves, give precise conditions for the existence of solitons
and write explicit solutions in the form of periodic waves. We also check that
the solitons observed previously in numerical simulations of the model
correspond exactly to our explicit solutions and see how plane waves
destabilize to form periodic waves.
