  In this talk we present investigation of the phase structure of a
(1+1)-dimensional quark model with four-quark interaction and in the presence
of baryon ($\mu_B$), isospin ($\mu_I$) and chiral isospin ($\mu_{I5}$) chemical
potentials. Spatially homogeneous and inhomogeneous (chiral density wave (for
chiral condensate) and single wave (for charged pion condensate)) condensates
are considered. It is established that in the large-$N_c$ limit ($N_c$ is the
number of colored quarks) there exists a duality correspondence between the
chiral symmetry breaking phase and the charged pion condensation one. The
primary conclusion of this investigation is the fact that chiral isospin
chemical potential generates charged pion condensation with non-zero baryon
density in dense quark matter. Moreover, it is shown that inhomogeneous charged
PC phase with nonzero baryon density is induced in the model by arbitrary small
values of the chemical potential $\mu_{I5}$ (for a rather large region of
$\mu_B$ and $\mu_I$).
