Mass-, and Energy-Preserving Sine Pseudo-Spectral Schemes with High-Accuracy for the Coupled Nonlinear Schrödinger Equation (Advances in Applied Mathematics and Mechanics, 2025)
In the paper, we consider the coupled nonlinear Schrödinger equation with high degree polynomials in the energy functional that cannot be handled by using thenewly proposed quadratic auxiliary variable method. Therefore, we develop the multiple quadratic auxiliary variable approach to deal with coupled systems and constructhigh-accuracy structure-preserving schemes for the equation. To fix the idea, we firstapply the multiple quadratic auxiliary variable approach to the equation and obtainan equivalent system that possesses the original energy and mass. Then, a family ofhigh-accuracy structure-preserving schemes that can conserve the mass and energy isderived by applying the Gauss collocation method and sine pseudo-spectral methodto approximate the system in time and space. The given schemes have high-accuracyin time and can both inherit the mass and Hamiltonian energy of the system. Amplenumerical results are given to confirm the accuracy and conservation of the developedschemes at last.