  General Relativity predicts two modes for plane gravitational waves. When a
tiny violation of Lorentz invariance occurs, the two gravitational wave modes
are modified. We use perturbation theory to study the detailed form of the
modifications to the two gravitational wave modes from the minimal
Lorentz-violation coupling. The perturbation solution for the metric
fluctuation up to the first order in Lorentz violation is discussed. Then, we
investigate the motions of test particles under the influence of the plane
gravitational waves with Lorentz violation. First-order deviations from the
usual motions are found.
