Theory of light-matter interaction in nematic liquid crystals and the   second Painlev\'e equation
  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 {\it shadow kink}. Its local profile is described by the second Painlev\'e equation. As part of our analysis we find new solutions to this equation thus generalizing the well known result of Hastings and McLeod. 
Marcel Clerc and Juan D\'avila and Micha{\l} Kowalczyk and Panayotis   Smyrnelis and Estefania Vidal-Henriquez
math.AP