Saddle-splay elasticity and field induced soliton in nematics

The symmetry breaking Fréedericksz transitions, when a uniformly aligned nematic state is replaced by a homogeneously or periodically distorted state, have been extensively studied before. Here we analyse the influence of the saddle-splay elasticity on the non-linear ground state of a nematic liquid crystal in the presence of a magnetic field above the Fréedericksz threshold. We identify the bifurcation point when the localized soliton-like state is linearly unstable with respect to the perturbations of the wavevector in the direction perpendicular to the initial plane of the soliton. This instability occurs only if the ratio of the saddle-splay elastic constant to the elastic modulus of nematics in the one-constant approximation is above the critical value K24/K\ ≥0.707