Nonlinear Dynamics

, Volume 68, Issue 1–2, pp 1–5 | Cite as

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

  • Igor V. Andrianov
  • Elena G. Kholod
  • Dieter Weichert
Original Paper


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.


Kink Improved continuum model Sine-Gordon equation Φ4 model Padé approximants 


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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Igor V. Andrianov
    • 1
  • Elena G. Kholod
    • 2
  • Dieter Weichert
    • 1
  1. 1.Department of General Mechanics, RWTHAachen UniversityAachenGermany
  2. 2.Department of Higher MathematicsDnipropetrovs’k University of Economics and LawDnipropetrovs’kUkraine

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