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.

中文翻译：

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高阶 Klein-Gordon-Schrödinger 方程的保守傅立叶频谱方案

摘要 本文提出了具有周期性边界条件的高阶Klein-Gordon-Schrodinger (KGS)系统的保守傅里叶谱方案。首先，使用空间中的傅立叶搭配方案，我们获得了高阶 KGS 系统的保守傅立叶谱方案。我们证明了所提出的方法完全满足离散质量和能量守恒定律。证明了数值解的存在唯一性，讨论了该方案的稳定性和收敛性。此外，我们发现该方案是解耦和非线性的。然后，我们给出了当 p = 1 时高阶 KGS 系统的线性化方案。数值实验验证了理论结果的正确性和方案的有效性。