Theory of light-matter interaction in nematic liquid crystals and the second Painlevé equation

Abstract

We study global minimizers of an energy functional arising as a thin sample limit in the theory of light-matter interaction in nematic liquid crystals. We show that depending on the parameters various defects are predicted by the model. In particular we show existence of a new type of topological defect which we call the shadow kink. Its local profile is described by the generalized Hastings and McLeod solutions of the second Painleve equation (Claeys et al. in Ann Math 168(2):601–641, 2008; Hastings and McLeod in Arch Ration Mech Anal 73(1):31–51, 1980). As part of our analysis we give a new proof of existence of these solutions.