  We present the results of an analytical and numerical study of the long-time
behavior for certain Fermi-Pasta-Ulam (FPU) lattices viewed as perturbations of
the completely integrable Toda lattice. Our main tools are the direct and
inverse scattering transforms for doubly-infinite Jacobi matrices, which are
well-known to linearize the Toda flow. We focus in particular on the evolution
of the associated scattering data under the perturbed vs. the unperturbed
equations. We find that the eigenvalues present initially in the scattering
data converge to new, slightly perturbed eigenvalues under the perturbed
dynamics of the lattice equation. To these eigenvalues correspond solitary
waves that emerge from the solitons in the initial data. We also find that new
eigenvalues emerge from the continuous spectrum as the lattice system is let to
evolve under the perturbed dynamics.
