A new conservative numerical method for strongly coupled nonlinear Schrödinger equations

In this paper, a numerical method based on the conservative finite difference scheme is constructed to numerically solve the strongly coupled nonlinear Schrödinger (SCNLS) equation. Conservative properties such as energy and mass of the SCNLS equation have been proven. In particular a fourth-order central difference scheme is used to discretize the the spatial derivative and a second-order Crank-Nicolson type discretization is used to discretize the temporal derivative. It has been shown that the proposed scheme preserves the discrete mass and energy. The existence of discrete solution is also investigated. Several numerical results are given to demonstrate the preservation properties of the new method. Also, the effect of the linear coupling parameters on the evolution of solitary waves is investigated.