  Steady transition fronts in nonlinear lattices are among the most important
dynamic coherent structures. We use the Fermi-Pasta-Ulam model with piecewise
linear nonlinearity to show that there are exactly three distinct classes of
such fronts which differ fundamentally in how (and whether) they produce and
transport oscillations. To make this Hamiltonian problem analytically
transparent, we construct a quasicontinuum approximation generating all three
types of fronts and then show that the interconnection between different
classes of fronts in the original discrete model is the same as in the
quasicontinuum model. The proposed framework unifies previous attempts to
classify the transition fronts as radiative, dispersive, topological or
compressive and categorizes them instead as different types of dynamic defects.
