Momentum conservation law in explicit symplectic integrators for nonlinear wave equations

The momentum conservation law in an explicit symplectic integrator for nonlinear wave equations is discussed. We show that the total momentum is approximately conserved within a numerical error on the order of the rounding error. We also perform numerical simulations to demonstrate the validity and numerical convergence of our expression for the total momentum. As a result, we show that a symplectic integrator for nonlinear wave equations possesses desirable properties of numerical methods, explicitness, and substantial conservation of the energy and total momentum. (author)