with η η taken to be the Gaussian white noise with mean zero and covariance E [ η η ( x , t ) η η ( x ′ , t ′ ) ] = δ δ ( x − − x ′ ) δ δ ( t − − t ′ ) . This is known as the Edwards–Wilkinson (EW) equation or stochastic heat equation with additive noise (SHE). Since this is a linear equation, it can be solved exactly by using Fourier analysis. But since the noise is Gaussian and the equation is linear, the fluctuations seen for this equation are still Gaussian. This means the EW equation is not enough to describe the surface growth of interest, so we need to add a nonlinear function for the growth. Therefore, surface growth change in time has three contributions. The first models lateral growth as a nonlinear function of the form F ( ∂ ∂ h ( x , t ) ∂ ∂ x ) . The second is a relaxation, or regularization, through the diffusion term ∂ ∂ 2 h ( x , t ) ∂ ∂ 2 x , and the third is the white noise forcing η η ( x , t ) . Therefore,