  We introduce a new approach to the study of modulation of high-frequency
periodic wave patterns, based on pseudodifferential analysis, multi-scale
expansion, and Kreiss symmetrizer estimates like those in hyperbolic and
hyperbolic-parabolic boundary-value theory. Key ingredients are local Floquet
transformation as a preconditioner removing large derivatives in the normal
direction of background rapidly oscillating fronts and the use of the periodic
Evans function of Gardner to connect spectral information on component periodic
waves to block structure of the resulting approximately constant-coefficient
resolvent ODEs. Our main result is bounded-time existence and valitidy to all
orders of large-amplitude smooth modulations of planar periodic solutions of
multi-D reaction diffusion systems in the high-frequency/small wavelength
limit.
