  We study the energy decay properties of a pulse propagating in a strongly
nonlinear granular chain with damping proportional to the relative velocity of
the grains. We observe a wave disturbance that at low viscosities consists of
two parts exhibiting two entirely different time scales of dissipation. One
part is an attenuating solitary wave, is dominated by discreteness and
nonlinearity effects as in a dissipationless chain, and has the shorter
lifetime. The other is a purely dissipative shocklike structure with a much
longer lifetime and exists only in the presence of dissipation. The range of
viscosities and initial configurations that lead to this complex wave
disturbance are explored.
