  The effect of explicit chiral-symmetry breaking on inhomogeneous chiral
phases is studied within a Nambu-Jona-Lasinio model with nonzero current quark
mass. Generalizing an earlier result obtained in the chiral limit, we show
within a Ginzburg-Landau analysis that the critical endpoint of the first-order
chiral phase boundary between two homogeneous phases gets replaced by a
"pseudo-Lifshitz point" when the possibility of inhomogeneous order parameters
is considered. Performing a stability analysis we also show that the unstable
mode along the phase boundary is in the scalar but not in the pseudoscalar
channel, suggesting that modulations which contain pseudoscalar condensates,
like a generalized dual chiral density wave, are disfavored against purely
scalar ones. Numerically we find that the inhomogeneous phase shrinks as one
moves away from the chiral limit, but survives even at significantly large
values of the current quark mass.
