2016/10/10 by Marcel Clerc, Marcel G. Clerc, Juan Dávila +8 · 1 citation
Computer Science · Materials Science · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #Liquid Crystal Research Advancements #Nonlinear Dynamics and Pattern Formation #Quantum chaos and dynamical systems #Stochastic processes and statistical mechanics #advanced mathematical theories #math.AP
paper · pdf · doi:10.48550/arxiv.1610.03044
openalex publication_date 2016/10/10 · arxiv created 2016/10/15 · arxiv updated 2016/10/18 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
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 Painlevé equation. As part of our analysis we find new solutions to this equation thus generalizing the well known result of Hastings and McLeod.