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...

The Mindlin model and hierarchical approach by Engelbrecht and Pastrone are used for modelling 1D wave propagation in microstructured solids. After introducing the free energy function, one gets from Euler–Lagrange equations a system of equations of motion. Making use of the slaving principle,...

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...