  This paper investigates the initial value problem for a system of
one-dimensional fourth-order dispersive partial differential-integral equations
with nonlinearity involving derivatives up to second order. Examples of the
system arise in relation with nonlinear science and geometric analysis.
Applying the energy method based on the idea of a gauge transformation and
Bona-Smith approximation technique, we prove that the initial value problem is
time-locally well-posed on the real line for initial data in a Sobolev space
with high regularity.
