Nonequilibrium Dynamics of the Complex Ginzburg-Landau Equation. I. Analytical Results

We present a detailed analytical and numerical study of nonequilibrium dynamics for the complex Ginzburg-Landau (CGL) equation. In particular, we characterize evolution morphologies using spiral defects. This paper (referred to as $\rm I$) is the first in a two-stage exposition. Here, we present analytical results for the correlation function arising from a single-spiral morphology. We also critically examine the utility of the Gaussian auxiliary field (GAF) ansatz in characterizing a multi-spiral morphology. In the next paper of this exposition (referred to as $\rm II$), we will present detailed numerical results.