  We discuss a short-time existence theorem of solutions to the initial value
problem for a fourth-order dispersive flow for curves parametrized by the real
line into a compact K\"ahler manifold. Our equations geometrically generalize a
physical model describing the motion of a vortex filament or the continuum
limit of the Heisenberg spin chain system. Our results are proved by using
so-called the energy method. We introduce a bounded gauge transform on the
pullback bundle, and make use of local smoothing effect of the dispersive flow
a little.
