Small dispersion limit of momentum conservation law

Abstract

Numerical properties of the momentum conservation law for Hamiltonian partial differential equations are investigated based on a symplectic time integration. In the nonlinear Klein–Gordon system, it is shown that the critical value of the coefficient of the dispersion term is nearly proportional to the inverse square of the total grid number. The result is consistent with the scale invariance of the equation of motion. On the other hand, in the nonlinear Schrödinger-type system, the critical value of the coefficient does not follow the scale invariance of the equation of motion.