Director precession and nonlinear waves in nematic liquid crystals under elliptic shear

Elliptic shear applied to a homeotropically oriented nematic above the elec tric bend Freedericks transition (FT) generates slow precession of the dire ctor. The character of the accompanying nonlinear waves changes from diffus ive phase waves to dispersive ones exhibiting spirals and spatiotemporal ch aos a!, the FT is approached from above. An exact solution of the now align ment equations captures the observed precession and predicts its reversal f or non-flow-aligning materials. The FT transforms into a Hopf bifurcation o pening the way to understand the wave phenomena.