The role of Painleve II in predicting new liquid crystal self-assembly mechanisms (Q1702441)

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.