Painlev\'e-II profile of the shadow kink in the theory of light-matter interaction in nematic liquid crystals

We confirm a prediction that the recently introduced shadow kink defect in the theory of light-matter interaction in nematic liquid crystals is described to main order by a solution of the Painlev\'e-II equation which changes sign once in the whole real line. Our result implies that such a solution of the latter equation is energy minimizing with respect to compactly supported perturbations.