  We analyze the nonlinear waves that propagate on a microtubule that is
tethered at its minus end due to kinesin walking on it, as is seen during the
fluid mixing caused by cytoplasmic streaming in Drosophila oocytes.The model we
use assumes that the microtubule can be modeled as an elastic string in a
viscous medium. The effect of the kinesin is to apply a force tangential to the
microtubule and we also consider the addition of a uniform cytoplasmic velocity
field. We show that travelling wave solutions exist and analyze their
properties. There exist scale invariant families of solutions and solutions can
exist that are flat or helical. The relationship between the period and
wavelength is obtained by both analytic and numerical means. Numerical
implementation of the equation of motion verifies our analytical predictions.
