The Ginzburg Landau formalism consisting of four globally coupled complex modulation equations is used to study instabilities of homogeneous states in axially anisotropic spatially extended systems that are infinite in two dimensions, when both critical wave numbers are nonzero, and the transition to instability involves imaginary growth rates and finite nonzero values of critical group velocities.
As an application, we present a bifurcation analysis of the weak electrolyte model for the electroconvection in nematic liquid crystals. A rich variety of patterns, like traveling waves, alternating waves and more complex spatiotemporal structures, is predicted at Hopf bifurcation, and compared with patterns observed experimentally. Eckhaus instability boundaries are determined, too.