LAUSR

Abstract In this paper, the conservative Fourier spectral scheme is presented for higher order Klein-Gordon-Schrodinger (KGS) system with periodic boundary condition. First, using the Fourier collocation scheme in space, we obtain an conservative Fourier spectral scheme for the higher order KGS system. We prove that the proposed method satisfies the discrete mass and energy conservation laws exactly. The existence and uniqueness of the numerical solution is proved, and the stability and convergence of the scheme is discussed. Moreover, we find the scheme is decoupled and nonlinear. Then, we give linearized scheme of the higher order KGS system when p = 1 . The numerical experiments are given to show that verify the correctness of theoretical results and the efficiency of the scheme.