A structure preserving numerical method for strongly coupled nonlinear Schrödinger system

In this thesis, a new structure-preserving numerical method for strongly coupled nonlinear Schrödinger equation (SCNLS) is presented. It is shown that the proposed new method conserves the discrete mass and energy. Numerical results are given to show the efficiency and effectiveness of the method and compared with the existing results in the literature. Numerical results show that the proposed method preserves both the mass and energy structure of the SCNLS equation up to the machine error and therefore has a better long-time behaviour.