  The time evolution of the scattering and spectral data is obtained for the
differential operator $\displaystyle\frac{d^4}{dx^4} +\displaystyle\frac{d}{dx}
u(x,t)\displaystyle\frac{d}{dx}+v(x,t),$ where $u(x,t)$ and $v(x,t)$ are
real-valued potentials decaying exponentially as $x\to\pm\infty$ at each fixed
$t.$ The result is relevant in a crucial step of the inverse scattering
transform method that is used in solving the initial-value problem for a pair
of coupled nonlinear partial differential equations satisfied by $u(x,t)$ and
$v(x,t).$
