Group analysis of equilibrium equations for a nematocholesteric

Abstract

We obtain a Lie algebra admitted by the system of equilibrium equations for a nematocholesteric, which models equilibrium configurations of the elastic field in the one-constant approximation of the continuum theory. In the case of a pure nematic, the system is found to admit a ten-dimensional Lie algebra, while in the case of a cholesteric, the system admits a four-dimensional Lie algebra. In addition, we have received particular analytical solutions of the system of model equations.