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