The role of Painleve II in predicting new liquid crystal self-assembly mechanisms
type: Item
instance of: scholarly article
title: The role of Painleve II in predicting new liquid crystal self-assembly mechanisms
zbMATH Open document ID: 1393.35210
author: W. C. Troy
published in: Archive for Rational Mechanics and Analysis
publication date: 2018-02-28T00:00:00Z
review text: The Painleve II equation \(w_{zz}=2w^3+zw+\alpha\) with a constant \(\alpha<0\) appears in description of nematic liquid crystals as well as in the modified Korteweg-de Vries equation. A new class of solutions, called shadow kinks is studied using topological shooting method. These are sign changing solutions which satisfy \(w(z)\sim -\sqrt{|z|/2}\) as \(z\to-\infty\), and \(w(z)\sim -\frac{\alpha}{z}\) as \(z\to\infty\). They play a critical role in the prediction of a new class of topological defects, one dimensional shadow kinks and two dimensional shadow vortices, in light-matter interaction experiments on nematic liquid crystals.
reviewed by: Piotr Biler
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 76A15
Mathematics Subject Classification ID: 35C08
Mathematics Subject Classification ID: 82D30
zbMATH DE Number: 6845146
zbMATH Keywords: Painleve equation
zbMATH Keywords: asymptotics
zbMATH Keywords: shooting method
zbMATH Keywords: nematic liquid crystals
MaRDI profile type: Publication
full work available at URL: s00205-017-1162-8
OpenAlex ID: W2746706557
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DOI: 10.1007/S00205-017-1162-8
description: scientific article; zbMATH DE number 6845146