Novel Multi-Symplectic Integrators for Nonlinear Fourth-Order Schrödinger Equationwith TrappedTerm

The multi-symplectic Runge-Kutta (MSRK) methods and multi-symplectic Fourier spectral (MSFS) methods will be employed to solve the fourth-order Schrödinger equations with trapped term. Using the idea of split-step numerical method and the MSRK methods, we devise a new kind of multi-symplectic integrators, which is called split-stepmulti-symplectic (SSMS)methods. The numerical experiments show that the proposed SSMSmethods aremore efficient than the conventional multi-symplectic integrators with respect to the the numerical accuracy and conservation perserving properties. AMS subject classifications: 65P10, 65M06, 65M70