Evolution of the order parameter in situations with broken rotational symmetry

We describe the evolution of the envelope of a wavetrain which, at a critical value of the stress parameter, breaks the rotational symmetry of the governing equations. The new envelope equation is a generalization to wavelike disturbances of the Newell-Whitehead-Segel equation and the one-dimensional complex Ginzburg-Landau equation. The most novel prediction of the new theory is that spatially uniform envelopes are rarely stable and that the dynamics is dominated by terms which c...onserve phase space volume. In particular, it turns out that the strongest spatial modulation takes place along the wave crests, perpendicular to the direction of the propagation. We also discuss mean drift effects and in particular their consequences near lateral boundaries.