Eckhaus Instability - Swift-Hohenberg Equation

Stripes + Random Squeezing Stripes + Random Perturbation

x-dependent random perturbation

general random perturbation

The Swift-Hohenberg equation is simulated with an initial state of stripes with wave number 1.178, just Eckhaus unstable, plus a small random perturbation. Since the perturbation is random you will see dynamics that differs in detail every time you repeat the simulation using the Reset button. Notice that the final result is the elimination of one or more roll pairs, although in the larger two dimensional simulation this usually occurs through the slow dynamics of dislocations.

It is instructive to switch between the real-space and Fourier plots