  We investigate the kinetics of nonlinear collision-induced fragmentation. We
obtain the fragment mass distribution analytically by utilizing its travelling
wave behavior. The system undergoes a shattering transition in which a finite
fraction of the mass is lost to infinitesimal fragments (dust). The nature of
the shattering transition depends on the fragmentation process. When the larger
of the two colliding fragments splits, the transition is discontinuous and the
entire mass is transformed into dust at the transition point. When the smaller
fragment splits, the transition is continuous with the dust gaining mass
steadily on the account of the fragments. At the transition point, the fragment
mass distribution diverges algebraically for small masses, c(m) ~ m^-a, with
a=1.20191.
