Interaction of solitary waves in confined granular alignments and the quasi-equilibrium state

We consider a chain of elastic beads, in which the individual grains repel upon contact according to the non-linear Hertz potential. We further assume that the chain is under zero loading, i.e., the grains barely touch one another. We show via careful numerical solution of the equations of motion that an impulse propagates as a solitary wave and that the collision of identical solitary waves propagating in opposite directions along the chain spawns a hierarchy of multiple weak solitary waves. We mention that the generated baby waves eventually must lead to a "volatile" equilibrium-like state, which we refer to as the quasi-equilibrium state.