  In this paper the phase structure of the dense quark matter has been
investigated in the presence of baryon ${\mu}_B$, isospin ${\mu}_I$, chiral
${\mu}_{5}$ and chiral isospin ${\mu}_{I5}$ chemical potentials in the
framework of Nambu--Jona-Lasinio model. It has been shown that in the
large-$N_{c}$ limit ($N_{c}$ is the number of quark colours) there exist three
duality correspondences in the model. The first duality is between the chiral
symmetry breaking and the charged pion condensation phenomena. And there are
two new dualities that hold only for chiral symmetry breaking and charged pion
condensation phenomena separately. It was shown that at nonzero chiral
${\mu}_{5}$ chemical potential chiral isospin ${\mu}_{I5}$ chemical potential
can generate charged pion condensation in dense quark matter even with zero
${\mu}_{I}$. But ${\mu}_{5}$ alone (in absence of ${\mu}_{I5}$ chemical
potential) can generate this phase but not as powerfully as ${\mu}_{I5}$ does
and only at comparatively low baryon densities.
