The modelling of wave propagation in microstructured materials should be able to account for various scales of microstructure. In the present paper governing equations for 1D waves in microstructured material are presented, based on the Mindlin model and the hierarchical approach. The governing equation under consideration has an analytical solution only in limit cases, therefore numerical analysis is carried out. Numerical solutions are found in the case of localized initial conditions by employing the pseudospectral method. Special attention is paid to the solitonic character of the solution.
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