  Currently, effective phonons (renormalized or interacting phonons) rather
than solitary waves (for short, solitons) are regarded as the energy carriers
in nonlinear lattices. In this work, by using the approximate soliton solutions
of the corresponding equations of motion and adopting the Boltzmann
distribution for these solitons, the average velocities of solitons are
obtained and are compared with the sound velocities of energy transfer.
Excellent agreements with the numerical results and the predictions of other
existing theories are shown in both the symmetric Fermi-Pasta-Ulam-$\beta$
lattices and the asymmetric Fermi-Pasta-Ulam-$\alpha \beta$ lattices. These
clearly indicate that solitons are suitable candidates for energy carriers in
Fermi-Pasta-Ulam lattices. In addition, the root-mean-square velocity of
solitons can be obtained from the effective phonons theory.
