Journal of Statistical Physics, Vol. 53, Nos. 5/6, 1988, p. 1031-1040.
The ground states of a certain class of one-dimensional models with a non-convex 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 Marchand et 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.