Equivalence of certain convex and nonconvex models of spatially modulated structures

The ground states of a certain class of one-dimensional models with a nonconvex interatomic interaction which exhibit spatially modulated structures are proved to be equivalent to those of the Frenkel-Kontorova-type models with a convex interatomic interaction. One of the nonconvex models numerically studied by Marchandet al. belongs to this class, and it turns out to be equivalent to the exactly solvable model with a complete devil's staircase studied by Aubry.