• Oleg M. Braun
  • Yuri S. Kivshar
Part of the Texts and Monographs in Physics book series (TMP)


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.


Topological Charge Substrate Potential Energy Static Kink Nonlinear Partial Differential Equa Constant Negative Gaussian Curvature 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Oleg M. Braun
    • 1
  • Yuri S. Kivshar
    • 2
  1. 1.Institute of PhysicsUkrainian Academy of SciencesKievUkraine
  2. 2.Research School of Physical Sciences and EngineeringAustralian National UniversityCanberraAustralia

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