line of length $L=40 \pi$. Panels [**(c)**]{}. Same as panel (a) but for the OS state obtained after the transition. Panel [**(d)**]{}. Time evolution of the wavefunction of the lowest energy state inside the condensate. Plotted quantities are in normalized units.[]{data-label="fig5"}](fig5b.eps "fig:"){width="4.2cm" height="4.6cm"}

![[**(a)**]{} Wavefunction of the intersite-asymmetric (IA) gap-soliton (thick line) plotted together with the wavefunctions of the lowest and first excited fermionic states trapped in the condensate (second and first curve from the top, respectively). The periodic potential, scaled by a factor 10 for graphical convenience, is also shown with a thin line at the bottom. Parameter values are the same as in Fig. \[fig3\] with $N_b=1$. [**(b)**]{} Time evolution of the bosonic and fermionic densities of the metastable IA gap-soliton obtained from the quasi-classical Eqs. (\[bose-fermi-eqns\]) on a line of length $L=40 \pi$. Panels [**(c)**]{}. Same as panel (a) but for the OS state obtained after the transition. Panel [**(d)**]{}. Time evolution of the wavefunction of the lowest energy state inside the condensate. Plotted quantities are in normalized units.[]{data-label="fig5"}](fig5c.eps "fig:"){width="4.2cm" height="4.2cm"} ![[**(a)**]{} Wavefunction of the intersite-asymmetric (IA) gap-soliton (thick line) plotted together with the wavefunctions of the lowest and first excited fermionic states trapped in the condensate 