from the condensate and with a change of symmetry of the wavefunction of the other fermion from IA to OS type (see second curves from the top in panels (a) and (c)). Similar phenomena occur for other metastable gap-solitons states existing in higher energy gaps and for different sign combinations of the interatomic interactions.

Also notice from Fig. \[fig5\]b that the IA-OS transition occurs with emission of matter from the condensate meaning that the final OS gap soliton state contains less matter than the initial state. This implies that the corresponding effective potential for the fermions is weaker after the transition and therefore less effective to hold a second bound state in the condensate. As the boson-fermion (attractive) interaction and the number of bosons in the gap soliton are increased, we find that more fermionic levels are able to enter the condensate.

An interesting problem to investigate is how a matter wave q-dot (gap soliton) gets progressively filled with fermions as the product $\chi_{bf}N_b$ is increased. To this regard we consider OS bosonic gap solitons with attractive boson-fermion interaction and with both repulsive and attractive boson-boson interactions.

-.5cm ![Left panel. Energy levels of the fermionic bound states inside the condensate 