A new method, involving the solution of a nonlinear eigenvalue equation, is proposed for finding the ground-state configurations and energies of the Frenkel-Kontorova and similar onedimensional models which can show complicated transitions between commensurate and incommensurate phases. It is used to show that a distinctive phase diagram can arise if a cosine potential is perturbed by the addition of suitable harmonics.

• Received 3 March 1986

DOI:https://doi.org/10.1103/PhysRevLett.56.1929