Recently inhomogeneous chiral phase (iCP) has been expected to appear in the moderate density region in the QCD phase diagram, where chiral condensate is spatially modulating. It has been known that axial anomaly and nesting play important roles for iCP. Using the Gross-Neveu models in 1+1 dimensions, we shall discuss axial anomaly and nesting from two different points of view:one is inhomogeneous chiral transition and the other is the Ferrel-Fulde-Larkin-Ovchinnikov state in superconductivity, which are closely related to each other by way of duality.