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Application of quasi-continuum models for perturbation analysis of discrete kinks

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Abstract

Here, we study a relation between discrete and continuum models on an example of the sine-Gordon and Φ 4 equations. The analysis of various receptions of continualization in a linear case is carried out. The best approach allowing describing all spectrum of the discrete one-dimensional medium is chosen. Also, the nonlinear discrete sine-Gordon and Φ 4 models are analyzed. The possibility of improvement of the known continuum approximations of these equations is shown.

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Authors and Affiliations

  1. Department of General Mechanics, RWTH, Aachen University, Templergraben 64, Aachen, 52062, Germany

    Igor V. Andrianov & Dieter Weichert

  2. Department of Higher Mathematics, Dnipropetrovs’k University of Economics and Law, Naberezhna Lenina 18, Dnipropetrovs’k, 49000, Ukraine

    Elena G. Kholod

Authors
  1. Igor V. Andrianov
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  2. Elena G. Kholod
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  3. Dieter Weichert
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Correspondence to Igor V. Andrianov.

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Andrianov, I.V., Kholod, E.G. & Weichert, D. Application of quasi-continuum models for perturbation analysis of discrete kinks. Nonlinear Dyn 68, 1–5 (2012). https://doi.org/10.1007/s11071-011-0198-9

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  • DOI: https://doi.org/10.1007/s11071-011-0198-9

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