  In this paper, we study the smooth transition from solitons to solitary waves
in localization, relation between energy and velocity, propagation and
scattering property in the Fermi-Pasta-Ulam lattice analytically and
numerically. A soliton is a very stable solitary wave that retains its
permanent structure after interacting with other solitary waves. A soliton
exists when the energy is small, and it becomes a solitary wave when the energy
increases to the threshold. The transition could help to understand the
distinctly different heat conduction behaviors of the Fermi-Pasta-Ulam lattice
at low and high temperature.
