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Saddle-splay elasticity and field induced soliton in nematics

The symmetry breaking Freedericksz 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 nematic liquid crystal in presence of magnetic field above the Freedericksz threshold. We identify the bifurcation point when the kink-soliton is linearly unstable with respect to the perturbations of the wave vector in the direction perpendicular to the initial plane of soliton. This instability occurs only if the ratio of saddle-splay elastic constant to elastic modulus of nematics in one-constant approximation is above the critical value |K_{24}/K|>0.707.