  We present the results of study of a nonlinear evolutionary PDE (more
precisely, a one-parameter family of PDEs) associated with the chain of
pre-stressed granules. The PDE in question supports solitary waves of
compression and rarefaction (bright and dark compactons) and can be written in
Hamiltonian form. We investigate {\em inter alia} integrability properties of
this PDE and its generalized symmetries and conservation laws.
  For the compacton solutions we perform a stability test followed by the
numerical study. In particular, we simulate the temporal evolution of a single
compacton, and the interactions of compacton pairs. The results of numerical
simulations performed for our model are compared with the numerical evolution
of corresponding Cauchy data for the discrete model of chain of pre-stressed
elastic granules.
