  We study the equilibrium time correlations for the conserved fields of
classical anharmonic chains and argue that their dynamic correlator can be
predicted on the basis of nonlinear fluctuating hydrodynamics. In fact our
scheme is more general and would cover also other one-dimensional hamiltonian
systems, for example classical and quantum fluids. Fluctuating hydrodynamics is
a nonlinear system of conservation laws with noise. For a single mode it is
equivalent to the noisy Burgers equation, for which explicit solutions are
available. Our focus is the case of several modes. No exact solutions have been
found so far and we rely on a one-loop approximation. The resulting
mode-coupling equations have a quadratic memory kernel and describe the time
evolving 3 x 3 correlator matrix of the locally conserved fields. Long time
asymptotics is computed analytically and finite time properties are obtained
through a numerical simulation of the mode-coupling equations.
