Symplectic Fourier pseudo-spectral schemes for Klein-Gordon-Schrödinger equation

Symplectic Fourier pseudo-spectral integrators for Klein-Gordon-Schrdinger equations(KGS) are investigated.A Hamiltonian formulation is presented.Fourier pseudo-spectral discretization is applied to the space approximation which leads to a finite-dimensional Hamiltonian system.Symplectic integrators,including Strmer/Verlet method and midpoint rule,are adopted in the time direction which leads to symplectic integrators for KGS.It suggests that the Strmer/Verlet method is explicit which can be coded effciently,and the midpoint rule captures mass of the original system exactly.Numerical experiments show that symplectic integrator can simulate various solitary well over a long period.