Phase instabilities in hexagonal patterns

Abstract

The general form of the amplitude equations for a hexagonal pattern including spatial terms is discussed. At the lowest order we obtain the phase equation for such patterns. The general expression of the di usion coe cients is given and the contributions of the new spatial terms are analysed in this paper. From these coe cients the phase stability regions in a hexagonal pattern are determined. In the case of B enard-Marangoni instability our results agree qualitatively with numerical simulations performed recently.