2016/10/10 by Marcel G. Clerc, Juan Dávila, Clerc, Marcel +7 · 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
paper · pdf · doi:10.48550/arxiv.1610.03044
openalex publication_date 2016/10/10 · 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\nlimit in the theory of light-matter interaction in nematic liquid crystals. We\nshow that depending on the parameters various defects are predicted by the\nmodel. In particular we show existence of a new type of topological defect\nwhich we call the it shadow kink. Its local profile is described by the\nsecond Painlev 'e equation. As part of our analysis we find new solutions to\nthis equation thus generalizing the well known result of Hastings and McLeod.\n