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Propagation of sech2-type solitary waves in hierarchical KdV-type systems

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  • Ilison, Lauri
  • Salupere, Andrus

Abstract

A hierarchical Korteweg–de Vries-type evolution equation is applied for modelling wave propagation in dilatant granular materials. The model equation is integrated numerically under sech2-type initial conditions using the Fourier transform-based pseudospectral method. Numerical simulations are carried out over a wide range of material parameters (two dispersion parameters and one microstructure parameter) and amplitudes of the initial wave. The analysis of the time–space behaviour of solutions results in five solution types. Besides typical KdV-like solitonic structures, wave packets were detected for some domains of material parameters.

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  • 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.
    • Handle: RePEc:eee:matcom:v:79:y:2009:i:11:p:3314-3327
    DOI: 10.1016/j.matcom.2009.05.003
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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. Tamm, Kert & Salupere, Andrus, 2012. "On the propagation of 1D solitary waves in Mindlin-type microstructured solids," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(7), pages 1308-1320.
    3. Mart Ratas & Jüri Majak & Andrus Salupere, 2021. "Solving Nonlinear Boundary Value Problems Using the Higher Order Haar Wavelet Method," Mathematics, MDPI, vol. 9(21), pages 1-12, November.

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