  We discuss a short-time existence theorem of solutions to the initial value
problem for a third order dispersive flow for closed curves into a compact
almost Hermitian manifold. Our equations geometrically generalize a physical
model describing the motion of vortex filament. The classical energy method
cannot work for this problem since the almost complex structure of the target
manifold is not supposed to be parallel with respect to the Levi-Civita
connection. In other words, a loss of one derivative arises from the covariant
derivative of the almost complex structure. To overcome this difficulty, we
introduce a bounded pseudodifferential operator acting on sections of the
pullback bundle, and eliminate the loss of one derivative from the partial
differential equation of the dispersive flow.
