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On solitons in microstructured solids and granular materials

Author

Listed:
  • Salupere, A.
  • Engelbrecht, J.
  • Ilison, O.
  • Ilison, L.

Abstract

The problems under consideration are related to wave propagation in nonlinear dispersive media, characterised by higher-order nonlinear and higher-order dispersive effects. Particularly two problems — wave propagation in dilatant granular materials and wave propagation in shape-memory alloys — are studied. Model equations are KdV-like evolution equations in both cases. The types of solutions are determined and analysed. It has been found that waves in granular materials are composed by two concurrent ensembles of solitary waves and there exist a threshold parameter value governing the behaviour of stable waves in alloy type materials.

Suggested Citation

  • Salupere, A. & Engelbrecht, J. & Ilison, O. & Ilison, L., 2005. "On solitons in microstructured solids and granular materials," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 69(5), pages 502-513.
    • Handle: RePEc:eee:matcom:v:69:y:2005:i:5:p:502-513
    DOI: 10.1016/j.matcom.2005.03.015
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    Cited by:

    1. Ilison, O. & Salupere, A., 2006. "On the propagation of solitary pulses in microstructured materials," Chaos, Solitons & Fractals, Elsevier, vol. 29(1), pages 202-214.
    2. Christov, Ivan C., 2012. "Hidden solitons in the Zabusky–Kruskal experiment: Analysis using the periodic, inverse scattering transform," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(6), pages 1069-1078.
    3. Ilison, Lauri & Salupere, Andrus, 2009. "Propagation of sech2-type solitary waves in hierarchical KdV-type systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(11), pages 3314-3327.

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