Novel multi-symplectic integrators for nonlinear fourth-order Schrödinger equation with trapped term

Abstract

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 SSMS methods are more efficient than the conventional multi-symplectic integrators with respect to the the numerical accuracy and conservation perserving properties. © 2010 Global-Science Press.