Discommensuration theory and shadowing in Frenkel–Kontorova models

We prove that if the minimum energy advancing discommensuration of mean spacing p / q for a Frenkel–Kontorova chain is unique up to translations and has phonon gap then all minimum energy states with mean spacing ω just above p / q are approximated exponentially well in q ω − p by concatenations of advancing p / q discommensurations.