Numerical Simulation of Interaction of Solitons and Solitary Waves in Granular Materials

摘要

A hierarchical Korteweg–de Vries type evolution equation is used for modelling of wave propagation in dilatant granular materials. The model equation is integrated numerically under sech~2-type initial conditions using the discrete Fourier transform based pseudospectral method. In our previous papers we have shown that depending on values of material parameters five different solution types can be detected. In all cases one component of the solution is a solitary wave or an ensemble of solitary waves (solitons) that can propagate at constatnt speed and amplitude and in cases of ensembles interact (almost) elastically. In the present paper additional numerical experiments for simulation of interactions between different soliton ensembles, single solitons and solitary waves are carried out and analysed.