A note on multisymplectic Fourier pseudospectral discretization for the nonlinear Schrödinger equation

Based on the multisymplectic Fourier pseudospectral scheme for the nonlinear Schrödinger (NLS) equation, we investigate some discrete properties corresponding to local conservation laws of the original equation. The discrete normal conservation law is proved, and the error estimation of local and global energy conservation laws are also obtained. Numerical experiments for cubic NLS equation are provided to demonstrate the consistency between the theoretical analysis and the numerical results.