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

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.