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On the propagation of solitary pulses in microstructured materials

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  • Ilison, O.
  • Salupere, A.

Abstract

KdV-type evolution equation, including the third- and the fifth-order dispersive and the fourth-order nonlinear terms, is used for modelling the wave propagation in microstructured solids like martensitic–austenitic alloys. The character of the dispersion depends on the signs of the third- and the fifth-order dispersion parameters. In the present paper the model equation is solved numerically under localised initial conditions in the case of mixed dispersion, i.e., the character of dispersion is normal for some wavenumbers and anomalous for others. Two types of solution are defined and discussed. Relatively small solitary waves result in irregular solution. However, if the amplitude exceeds a certain threshold a solution having regular time–space behaviour emerges. The latter has tree sub-types: “plaited” solitons, two solitary waves and single solitary wave. Depending on the value of the amplitude of the initial pulse these sub-types can appear alone or in a certain sequence.

Suggested Citation

  • Ilison, O. & Salupere, A., 2006. "On the propagation of solitary pulses in microstructured materials," Chaos, Solitons & Fractals, Elsevier, vol. 29(1), pages 202-214.
    • Handle: RePEc:eee:chsofr:v:29:y:2006:i:1:p:202-214
    DOI: 10.1016/j.chaos.2005.08.048
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    References listed on IDEAS

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    1. Ilison, O. & Salupere, A., 2005. "Propagation of sech2-type solitary waves in higher-order KdV-type systems," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 453-465.
    2. 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.
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    Cited by:

    1. Abourabia, A.M. & El-Danaf, T.S. & Morad, A.M., 2009. "Exact solutions of the hierarchical Korteweg–de Vries equation of microstructured granular materials," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 716-726.
    2. Tamm, Kert & Peets, Tanel, 2015. "On solitary waves in case of amplitude-dependent nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 73(C), pages 108-114.

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