Painlevé-II profile of the shadow kink in the theory of light-matter interaction in nematic liquid crystals

Abstract

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 Painlevé-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.

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

References in corpus (2)

• Thomas-Fermi approximation for coexisting two component Bose-Einstein condensates and nonexistence of vortices for small rotation
• Symmetry breaking and restoration in the Ginzburg-Landau model of nematic liquid crystals