  With focus on anharmonic chains, we develop a nonlinear version of
fluctuating hydrodynamics, in which the Euler currents are kept to second order
in the deviations from equilibrium and dissipation plus noise are added. The
required model-dependent parameters are written in such a way that they can be
computed numerically within seconds, once the interaction potential, pressure,
and temperature are given. In principle the theory is applicable to any
one-dimensional system with local conservation laws. The resulting nonlinear
stochastic field theory is handled in the one-loop approximation. Some of the
large scale predictions can still be worked out analytically. For more details
one has to rely on numerical simulations of the corresponding mode-coupling
equations. In this way we arrive at detailed predictions for the equilibrium
time correlations of the locally conserved fields of an anharmonic chain.
