  Solitary waves (SWs) are generated in monoatomic (homogeneous) lightly
contacting spherical granules by an applied input force of any time-variation
and intensity. We consider finite duration shock loads and focus on the
transition regime that leads to the formation of SWs. Based on geometrical and
material properties of the granules and the properties of the input shock, we
provide explicit analytic expressions to calculate the peak value of the
compressive contact force at each contact point in the transition regime that
precedes the formation of a primary solitary wave. We also provide explicit
expressions to estimate the number of granules involved in the transition
regime and show its dependence on the characteristics of the input shock and
material/geometrical properties of the interacting granules. Finally, we assess
the accuracy of our theoretical results by comparing them with those obtained
through numerical integration of the equations of motion.
