Theory of light-matter interaction in nematic liquid crystals and the second Painlev\'e equation

TL;DR

This paper investigates the energy minimizers in nematic liquid crystals, revealing new defect types like the shadow kink described by the second Painlevé equation, and extends solutions to this equation.

Contribution

It introduces a novel defect called the shadow kink and links its profile to the second Painlevé equation, expanding the understanding of light-matter interactions in liquid crystals.

Findings

Existence of a new defect type called the shadow kink.

Profile of the shadow kink described by the second Painlevé equation.

New solutions to the second Painlevé equation generalizing Hastings and McLeod.

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 {\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.