  As an application of Gradient Expansion (long-wavelength) approximation, we
studied the inhomogeneous universe including the gravitational wave(GW). For a
plane-symmetric cosmological model, we could implement the 2nd order expansion
and analyze the purely non-linear perturbation of GW. The result indicates that
the non-linear effect plays an important role in anisotropic stage of the
universe. We also confirm that the perturbation from the linear source term in
gradient expansion is consistent with the result of linear perturbation.
