Orientation Waves in a Director Field With Rotational Inertia

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dc.creatorAli, Giuseppe
dc.creatorHunter, John K.
dc.date2006-09-07
dc.date.accessioned2026-07-07T07:24:35Z
dc.date.available2026-07-07T07:24:35Z
dc.descriptionWe study the propagation of orientation waves in a director field with rotational inertia and potential energy given by the Oseen-Frank energy functional from the continuum theory of nematic liquid crystals. There are two types of waves, which we call splay and twist waves. Weakly nonlinear splay waves are described by the quadratically nonlinear Hunter-Saxton equation. Here, we show that weakly nonlinear twist waves are described by a new cubically nonlinear, completely integrable asymptotic equation. This equation provides a surprising representation of the Hunter-Saxton equation as an advection equation. There is an analogous representation of the Camassa-Holm equation. We use the asymptotic equation to analyze a one-dimensional initial value problem for the director-field equations with twist-wave initial data.
dc.identifierhttps://arxiv.org/abs/math/0609189
dc.identifierhttp://arxiv.org/abs/math/0609189
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/116412
dc.subjectAnalysis of PDEs
dc.subjectMathematical Physics
dc.subject35L70; 37K10
dc.titleOrientation Waves in a Director Field With Rotational Inertia
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