Pattern formation with Galilean symmetry

The behaviour of pattern-forming systems in one dimension with Galilean symmetry in large domains is not described by the usual Ginzburg-Landau equation. This is because the Galilean symmetry leads to a large-scale neutral mode that interacts with the pattern. The resulting coupled amplitude equations, derived by considering the symmetry, show chaotic behaviour and exhibit a novel scaling in which the amplitude of the pattern is proportional to the 3/4 power of the bifurcation parameter.