Numerical simulation of propagation of solitary deformation waves in a compressible hyperelastic rod

In this paper, propagation of axisymmetric deformation waves in circular cylindrical rods of compressible hyperelastic material is studied. The corresponding model equation that describes propagation of waves of moderate wave-length takes into account the coupling effect of the material nonlinearity and the geometric size of the rod. The model equation is integrated numerically under sech2-type initial conditions making use of the discrete Fourier transform based pseudospectral method. Numerical simulations are carried out over a wide range of material parameters. The analysis of the time-space behaviour of solutions demonstrates that in some domains of space of material parameters single solitary wave solutions or trains of interacting solitons can be emerged from the initial localised pulses.