Singular perturbation theory for phase-front dynamics and pattern selection

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Abstract
A class of phase-front dynamics equations is investigated through a particular singular perturbative expansion in a late-time, restricted-wavelength limit. The approximate solution provides a detailed description of the dynamics of pattern formation in all dimensions and reproduces some aspects of marginal stability theory in one dimension. A universal form for the dynamic structure factor is obtained for non-conserved systems. The results are applied to a model of the onset of the Rayleigh-Benard instability, the Swift-Hohenberg equation (1977).