Momentum conservation law in explicit symplectic integrators for a nonlinear Schrödinger-type equation

This paper discusses the momentum conservation law in a symplectic integrator for a nonlinear Schrödinger-type equation. We show that the total momentum, which is formally expressed by a polynomial of a discrete variable, is conserved under cyclic boundary conditions. We also perform numerical simulations to demonstrate the validity and numerical convergence of our expression for the total momentum. As a result, the symplectic integrator simultaneously satisfies the energy, density and momentum conservation laws. (author)