Globally Coupled Ginzburg Landau Equations for Electroconvection in Nematic Liquid Crystals*

For certain materials, the electrohydrodynamic instability leading to convection in nematic liquid crystals is a Hopf bifurcation with four critical wave numbers. As a consequence, the linearized problem admits solutions in the form of two pairs of oblique counterpropagating travelling rolls. To describe this instability in a weakly nonlinear analysis, a system of four globally coupled Ginzburg Landau equations is introduced, whose coefficients can be computed from the weak electrolyte model of Kramer and Treiber. Some aspects of the solution behaviour of this system are discussed and related to recent experiments conducted at Kent State University for the nematic I52.