  We study the Intermediate Scattering Function (ISF) of the strongly-nonlinear
Fermi-Pasta Ulam Model at thermal equilibrium, using both numerical and
analytical methods. From the molecular dynamics simulations we distinguish two
limit regimes, as the system behaves as an ideal gas at high temperature and as
a harmonic chain for low excitations. At intermediate temperatures the ISF
relaxes to equilibrium in a nontrivial fashion. We then calculate analytically
the Taylor coefficients of the ISF to arbitrarily high orders (the specific,
simple shape of the two-body interaction allows us to derive an iterative
scheme for these.) The results of the recursion are in good agreement with the
numerical ones. Via an estimate of the complete series expansion of the
scattering function, we can reconstruct within a certain temperature range its
coarse-grained dynamics. This is governed by a memory-dependent Generalized
Langevin Equation (GLE), which can be derived via projection operator
techniques. Moreover, by analyzing the first series coefficients of the ISF, we
can extract a parameter associated to the strength of the memory effects in the
dynamics.
