A two-component nonlinear variational wave system

2021/09/07 by Peder Aursand, Aursand, Peder, Anders Nordli +1
Materials Science · Mathematics · Physics and Astronomy · #35L51 #35Q35 #Advanced Differential Equations and Dynamical Systems #Analysis of PDEs (math.AP) #FOS: Mathematics #Liquid Crystal Research Advancements #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2109.02983

openalex publication_date 2021/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We derive a novel two-component generalization of the nonlinear variational wave equation as a model for the director field of a nematic liquid crystal with a variable order parameter. The two-component nonlinear variational wave equation admits solutions locally in time. We show that a particular long time asymptotic expansion around a constant state in a moving frame satisfy the two-component Hunter--Saxton system.

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