Local energy-preserving and momentum-preserving algorithms for coupled nonlinear Schrödinger system

In this paper, local energy and momentum conservation laws are proposed for the coupled nonlinear Schrödinger system. The two local conservation laws are more essential than global conservation laws since they are independent of the boundary conditions. Based on the rule that numerical algorithms should conserve the intrinsic properties of the original problems as much as possible, we propose local energy-preserving and momentum-preserving algorithms for the problem. The proposed algorithms conserve the local energy and momentum conservation laws in any local time–space region, respectively. With periodic boundary conditions, we prove the proposed algorithms admit the charge, global energy and global momentum conservation laws. Numerical experiments are conducted to show the performance of the proposed methods. Numerical results verify the theoretical analysis.