  We consider a hydrodynamic-type system of balance equations which is closed
by the dynamic equation of state taking into account the effects of spatial
nonlocality. Symmetry and local conservation laws of this system are studied. A
system of ODEs being obtained via the group theory reduction of the initial
system of PDEs is investigated. The reduced system is shown to possess a family
of the homoclinic solutions. Depending on the values of the parameters, the
homoclinic solutions describe the solitary waves of compression or
rarefication. The solutions corresponding to the wave of compression are shown
to be unstable. More likely, the waves of rarefication are stable. Numerical
simulations demonstrate that the solitary waves of rarefication moving toward
each other maintain their shape after the interaction.
