Inhomogeneous charged pion condensation phenomenon in the NJL$_2$ model   with quark number and isospin chemical potentials
  The properties of two-flavored massive Nambu--Jona-Lasinio model in (1+1)-dimensional spacetime are investigated in the presence of isospin and quark number chemical potentials. The consideration is performed in the large-$N_c$ limit, where $N_c$ is the number of colored quarks. It is shown in the framework of this model that charged pion condensation phenomenon of dense quark/hadron isotopically asymmetric matter is rather a spatially inhomogeneous than a homogeneous one. 
N. V. Gubina, K. G. Klimenko, S. G. Kurbanov, and V. Ch. Zhukovsky
hep-ph hep-th