We apply the method of invariant manifolds to derive equations of generalized
hydrodynamics from the linearized Boltzmann equation and determine exact
transport coefficients, obeying Green-Kubo formulas. Numerical calculations are
performed in the special case of Maxwell molecules. We investigate, through the
comparison with experimental data and former approaches, the spectrum of
density fluctuations and address the regime of finite Knudsen numbers and
finite frequencies hydrodynamics.Comment: This is a more detailed version of a related paper: I.V. Karlin, M.
Colangeli, M. Kroger, PRL 100 (2008) 214503, arXiv:0801.2932. It contains
comparison between predictions and experiment, in particular. 11 pages, 6
figures, 2 table