A two-component nonlinear variational wave system
Peder Aursand, Anders Nordli
TL;DR
This paper introduces a new two-component nonlinear variational wave system modeling nematic liquid crystals with variable order, demonstrating local solutions and connecting to the Hunter--Saxton system through asymptotic analysis.
Contribution
It presents a novel two-component generalization of the nonlinear variational wave equation for nematic liquid crystals, including local existence results and asymptotic connections.
Findings
Existence of local solutions for the two-component system
Derivation of a long-time asymptotic expansion
Connection to the Hunter--Saxton system
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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Taxonomy
TopicsNonlinear Waves and Solitons · Liquid Crystal Research Advancements · Advanced Differential Equations and Dynamical Systems