In the paper, the symplectic‐preserving Fourier spectral scheme is presented for space fractional Klein–Gordon–Schrödinger equations involving fractional Laplacian. First, we validate space fractional Klein–Gordon–Schrödinger equations that can be expressed as an infinite dimension Hamiltonian system. We apply the Fourier spectral method in space, and the semi‐discrete system preserves the mass and energy conservation laws. Second, by introducing some variables, the semi‐discrete system can be expressed as a large Hamiltonian ordinary differential system. We use the midpoint rule in time to semi‐discrete system, and obtain a symplectic approximation scheme of these equations. Moreover, we can prove that the scheme is convergent. To reduce the computational cost, we introduce the splitting idea for the symplectic integrators. Finally, we give numerical experiments to show the efficiency of the scheme.

中文翻译：

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空间分数Klein-Gordon-Schrödinger方程的保辛傅立叶谱格式

在本文中，提出了关于分数分数Laplacian的空间分数Klein-Gordon-Schrödinger方程的保辛傅立叶谱方案。首先，我们验证空间分数Klein-Gordon-Schrödinger方程，该方程可以表示为无限维哈密顿系统。我们在空间中应用傅立叶光谱方法，并且半离散系统保留了质量守恒和能量守恒定律。其次，通过引入一些变量，半离散系统可以表示为大型哈密顿常微分系统。我们将中点规则及时应用于半离散系统，并获得这些方程的辛逼近方案。此外，我们可以证明该方案是收敛的。为了降低计算成本，我们为辛积分器引入了分裂思想。最后，