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Nonlinear Science at the Dawn of the 21st Century pp 265–291Cite as

Nonlinear Models for the Dynamics of Topological Defects in Solids

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Abstract

We discuss several physical systems, where the nonlinear dynamics of topological defects is described by quasi-one-dimensional kink solutions of the generalized Frenkel-Kontorova model and its continuous approximations (the sine-Gordon equation). This includes dislocations, long Josephson junctions, magnetic chains, adsorbed layers of atoms, hydrogen-bonded chains, DNA-type chains, etc.We briefly review different properties of kinks and describe experimental verifications of kink dynamics.

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Authors
  1. Yuri S. Kivshar
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  2. Hartmut Benner
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  3. Oleg M. Braun
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  1. Department of Mathematical Modelling, The Technical University of Denmark, Building 321, 2800, Kgs. Lyngby, Denmark

    P. L. Christiansen , M. P. Sørensen  & A. C. Scott ,  & 

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Kivshar, Y.S., Benner, H., Braun, O.M. (2000). Nonlinear Models for the Dynamics of Topological Defects in Solids. In: Christiansen, P.L., Sørensen, M.P., Scott, A.C. (eds) Nonlinear Science at the Dawn of the 21st Century. Lecture Notes in Physics, vol 542. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46629-0_13

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