Symplectic-preserving Fourier spectral scheme for space fractionalKlein-Gordon-Schrodingerequations

In the paper, the symplectic-preserving Fourier spectral scheme is presented for space fractional Klein-Gordon-Schrodinger equations involving fractional Laplacian. First, we validate space fractional Klein-Gordon-Schrodinger 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.

Automated summary

In this paper, a symplectic-preserving Fourier spectral scheme is introduced for solving space fractional Klein-Gordon-Schrodinger equations involving fractional Laplacian. By using the midpoint rule, the semi-discrete system is transformed into a symplectic approximation scheme, and its convergence is proven. The splitting idea further reduces computational cost.