Solitary waves in continuum media pass through each other with only a slight phase change. However, in an intrinsically nonlinear many-body system such solitary waves could behave differently. It was predicted and experimentally confirmed that head-on solitary wave collisions in granular alignments are followed by the formation of tiny secondary solitary waves in the vicinity of the collision point. While it remains a challenge to provide an analytical treatment of the local time evolution, we present arguments and associated simulations to address a crucial unknown, namely, why the secondary solitary waves must form. Extensive numerical investigations on solitary wave collisions at a grain center and at an edge show marked differences. The effects of softening the grain repulsion are discussed to validate the arguments. © 2009 The American Physical Society.