This introductory chapter is intended to provide a general overview of the classical formulation of the Frenkel-Kontorova model and its continuum version, the sine-Gordon equation. The chapter introduces also the fundamental modes of the model, phonons, kinks, and breathers, and describes some of their general properties. It also provides the background for the subsequent discussion of the basic physical systems where the nonlinear dynamics is described by the Frenkel-Kontorova model and its generalizations.
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