Nonlinear phase diffusion equations for the long-wave instabilities of hexagons Original Research Article

The phase instabilities of hexagons are studied using the lowest order amplitude equations. The shapes of the unstable modes and the nonlinear phase diffusion equations which hold close to onset are found. The latter show that the instabilities are subcritical. It is found that the long-wave zigzag and two-dimensional Eckhaus instabilities cannot occur in hexagons.