  We investigate the form of equilibrium spatio-temporal correlation functions
of conserved quantities, and of energy transport in the Toda lattice and in
other integrable models. From numerical simulations we find that the
correlations satisfy ballistic scaling with a remarkable collapse of data from
different times. We examine special limiting choices of parameter values, for
which the Toda lattice tends to either the harmonic chain or the equal mass
hard-particle gas. In both these limiting cases, one can obtain the
correlations exactly and we find excellent agreement with the direct Toda
simulation results. We also discuss a transformation to "normal mode"
variables, as commonly done in hydrodynamic theory of non-integrable systems,
and find that this is useful, to some extent, even for the integrable system.
