  Small-amplitude waves in the Fermi-Pasta-Ulam (FPU) lattice with weakly
anharmonic interaction potentials are described by the generalized Korteweg-de
Vries (KdV) equation. Justification of the small-amplitude approximation is
usually performed on the time scale, for which dynamics of the KdV equation is
defined. We show how to extend justification analysis on longer time intervals
provided dynamics of the generalized KdV equation is globally well-posed in
Sobolev spaces and either the Sobolev norms are globally bounded or they grow
at most polynomially. The time intervals are extended respectively by the
logarithmic or double logarithmic factors in terms of the small amplitude
parameter. Controlling the approximation error on longer time intervals allows
us to deduce nonlinear metastability of small FPU solitary waves from orbital
stability of the KdV solitary waves.
