Propagation of sech-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.