Physics And Mathematics of Nonlinear Phenomena 2017

Within the framework of Oseen-Frank theory, we analyze the static confgurations for chiral liquid crystals. In particular, we find numerical solutions for localized axisymmetric states in confned chiral liquid crystals with weak homeotropic anchoring at the boundaries. These solutions describe the distortions of two-dimensional skyrmions, known as either spherulites or cholesteric bubbles, which have been observed experimentally in these systems. Relations with nonlinear integrable equations have been outlined and are used to study asymptotic behaviours of the solutions. By using analytical methods, we build approximated solutions of the equilibrium equations and we analyze the generation and stabilization of these states in relation to the material parameters, the external felds and the anchoring boundary conditions.