Christos Sourdis
Published 2018-11-19, updated 2019-04-15Version 2
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.
Comments: Refined the last part of the proof of Thm. 2.1, which implies more precise statements in Thm. 1.1 and Cor. 1.2. The minor changes start from the definition of the interval $J$ which is taken to be smaller (depending on N>1). Corrected an obvious misquotation of the main result in Clerc et al. (Calc. Var. 2017) in the introduction. Added discussion following Cor. 1.2
Theory of light-matter interaction in nematic liquid crystals and the second Painlevé equation
Dimensional Reduction and emergence of defects in the Oseen-Frank model for nematic liquid crystals
On the long-time behavior of some mathematical models for nematic liquid crystals
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