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Propagation of sech2-type solitary waves in higher-order KdV-type systems

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  • Ilison, O.
  • Salupere, A.

Abstract

Wave propagation in microstructured media is essentially influenced by nonlinear and dispersive effects. The simplest model governing these effects results in the Korteweg–de Vries (KdV) equation. In the present paper a KdV-type evolution equation, including the third- and fifth-order dispersive and the fourth-order nonlinear terms, is used for modelling the wave propagation in microstructured solids like martensitic–austenitic alloys. The model equation is solved numerically under localised initial conditions. Possible solution types are defined and discussed. The existence of a threshold is established. Below the threshold, the relatively small solitary waves decay in time. However, if the amplitude exceeds a certain threshold, i.e., the critical value, then such a solitary wave can propagate with nearly a constant speed and amplitude and consequently conserve the energy.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:26:y:2005:i:2:p:453-465
    DOI: 10.1016/j.chaos.2004.12.045
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    Cited by:

    1. Korkmaz, Alper & Dağ, İdris, 2009. "Crank-Nicolson – Differential quadrature algorithms for the Kawahara equation," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 65-73.
    2. Ilison, O. & Salupere, A., 2006. "On the propagation of solitary pulses in microstructured materials," Chaos, Solitons & Fractals, Elsevier, vol. 29(1), pages 202-214.

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