The Eckhaus instability in hexagonal patterns
The Eckhaus instability of hexagonal patterns is studied within the model of three coupled envelope equations for the underlying roll systems. The regions of instability in the parameter space are found analytically from both the phase approximation and a full system of amplitude equations. Beyond the stability limits of hexagons, two different modes go unstable. Both provide symmetry breaking of an initially regular pattern via splitting of a triplet of rolls into two triplets of growing disturbances. The parameters of fastest growing disturbances (wavelength, orientation, growth rate) are determined from the full set of linearized amplitude equations. The nonlinear stage of Eckhaus instability is investigated numerically.
scientific article; zbMATH DE number 710195