PHASE INSTABILITIES IN HEXAGONAL PATTERNS

The general form of the amplitude equations for a hexagonal pattern in cluding spatial terms is discussed. At the lowest order we obtain the phase equation for such patterns. The general expression of the diffus ion coefficients is given and the contributions of the new spatial ter ms are analysed in this paper. From these coefficients the phase stabi lity regions in a hexagonal pattern are determined. In the case of Ben ard-Marangoni instability our results agree qualitatively with numeric al simulations performed recently.