Non-uniform localised distortions in generalised elasticity for liquid crystals

We analyse a recent generalised free-energy for liquid crystals posited by Virga and falling in the class of quartic functionals in the spatial gradients of the nematic director. We review some known interesting solutions, i. e., uniform heliconical structures, and we find new liquid crystal configurations, which closely resemble some novel, experimentally detected, structures called Skyrmion tubes. These new configurations are characterised by a localised pattern given by the variation of the conical angle. We study the equilibrium differential equations and find numerical solutions and analytical approximations.