A conservative Fourier pseudospectral algorithm for a coupled nonlinear Schrödinger system

We derive a new method for coupled nonlinear Schrödinger system by using the square of first-order Fourier spectral differentiation matrix D₁ instead of traditional second-order Fourier spectral differentiation matrix D₂ to approximate second derivative. We prove the proposed method preserves the charge and energy conservation laws exactly. In numerical tests, we display the accuracy of numerical solution and the role of the nonlinear coupling parameter in cases of solitons collision. Numerical experiments also exhibit the excellent performance of the method in preserving the charge and energy conservation laws. These numerical results verify that the proposed method is both a charge-preserving and an energy-preserving algorithm.