Beyond the Ginzburg-Landau equation

From the foregoing discussion we know that the weakly non-linear behaviour of EHC in the range of validity of the GLE is imderstood fairly well. The situation is not quite as satisfactory when it comes to secondary bifurcations, which confine the q- range and which are captured in the theory only if corrections to GLE are included (Section 13.3) or a frill evaluation is done to the hydrodynamic equations. 

From the most recent experiments it is quite clear that, beginning with normal rolls at threshold and increasing e, the ZZ instability, where long wavelength modulations with wave-vector = (0, iy) perpendicular to q = (q, 0) start growing, provides the most impor- 

We only mention in passing that various undulated structures have been reported by Ribotta and co-workers [17, 105] but could not always be reproduced by others [169], Actually such structures can be obtained near the LP even within the GLE approximation, but they then turn out to be metastable since their (generalized) potential is higher than that of straight (usually oblique) rolls [14, 89, 90, 109, 110], This may explain why they are difficult to observe. 

---