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We study the equilibrium time correlations for the conserved fields ofclassical anharmonic chains and argue that their dynamic correlator can bepredicted on the basis of nonlinear fluctuating hydrodynamics. In fact ourscheme is more general and would cover also other one-dimensional hamiltoniansystems, for example classical and quantum fluids. Fluctuating hydrodynamics isa nonlinear system of conservation laws with noise. For a single mode it isequivalent to the noisy Burgers equation, for which explicit solutions areavailable. Our focus is the case of several modes. No exact solutions have beenfound so far and we rely on a one-loop approximation. The resultingmode-coupling equations have a quadratic memory kernel and describe the timeevolving 3 x 3 correlator matrix of the locally conserved fields. Long timeasymptotics is computed analytically and finite time properties are obtainedthrough a numerical simulation of the mode-coupling equations.

Dynamic Correlators of Fermi-Pasta-Ulam Chains and Nonlinear Fluctuating Hydrodynamics