Numerical simulation of coupled nonlinear Schrödinger equation
Mathematics and Computers in Simulation
A linearly implicit conservative scheme for the coupled nonlinear Schrödinger equation
Mathematics and Computers in Simulation
Mathematics and Computers in Simulation
Strong coupling of Schrödinger equations: Conservative scheme approach
Mathematics and Computers in Simulation
New schemes for the coupled nonlinear Schrodinger equation
International Journal of Computer Mathematics
Hi-index | 31.45 |
In this paper, local energy and momentum conservation laws are proposed for the coupled nonlinear Schrodinger 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.