  A regularization of the Cross-Newell equation is presented. It is based on a
secondary re-modulation along characteristics. This new characteristic
Cross-Newell equation is not isotropic (has preferred directions), but is
universal (homogeneous in $\eps$ and equation independent coefficients), has
fourth derivatives, and generates localized solutions that are bi-asymptotic to
rolls. Re-modulation of rolls in the Ginzburg-Landau equation is used for
illustration of the theory.
