Stability of non-equilateral hexagonal patterns governed by generalized amplitude equations

We consider the evolution of hexagonal convection patterns governed by non-potential amplitude equations in the particular case of the Boussinesq approximation. The amplitude equations contain new terms which can produce non-equilateral hexagonal patterns based on a resonant triad with different lengths of wave vectors. The stability regions of different kinds of patterns have been obtained. Non-stationary solutions are also studied.