A complete solution of the mathematical problem for the behaviour of the flexoelectric domains in a d.c. voltage for the case of anisotropic elasticity

The solution of the Euler-Lagrange equations for the director components n(y)=f(1)(z)sinqy and n(z)=f(2)(z)cosqy, where q is the wave number of the flexoelectric domains of Vistin'-Pikin-Bobylev, has been for the first time exactly found with the aid of matrix calculations for the case of a planar nematic layer with anisotropic elasticity and a negative dielectric anisotropy under the action of an inhomogeneous d.c. flexoelectrically deforming electric field. A comparison is made with another, approximate, solution for anisotropic elasticity and a homogeneous electric field. A discussion of the eventual applications of this solution is also presented.