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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.
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Griffiths et al. (1986) studied this question.
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