  The properties of the two-flavored Gross-Neveu model with nonzero current
quark mass are investigated in the (1+1)-dimensional spacetime at finite
isospin $\mu_I$ as well as quark number $\mu$ chemical potentials and zero
temperature. The consideration is performed in the limit $N_c\to\infty$, i.e.
in the case with an infinite number of colored quarks. In the plane of
parameters $\mu_I,\mu$ a rather rich phase structure is found, which contains
phases with and without pion condensation. We have found a great variety of
one-quark excitations of these phases, including gapless and gapped
quasiparticles. Moreover, the mesonic mass spectrum in each phase is also
investigated.
