  Elliptic shear applied to a homeotropically oriented nematic above the
electric bend Freedericks transition (FT) generates slow precession of the
director. The character of the accompanying nonlinear waves changes from
diffusive phase waves to dispersive ones exhibiting spirals and spatio-temporal
chaos as the FT is approached from above. An exact solution of the flow
alignment equations captures the observed precession and predicts its reversal
for non-flow aligning materials. The FT transforms into a Hopf bifurcation
opening the way to understand the wave phenomena.
