@Article{AAMM-17-1430,
author = {Fu , YayunZhang , GengenQian , Xu and Song , Songhe},
title = {Mass-, and Energy-Preserving Sine Pseudo-Spectral Schemes with High-Accuracy for the Coupled Nonlinear Schrödinger Equation},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2025},
volume = {17},
number = {5},
pages = {1430--1455},
abstract = {<p style="text-align: justify;">In the paper, we consider the coupled nonlinear Schrödinger equation with high degree polynomials in the energy functional that cannot be handled by using the
newly proposed quadratic auxiliary variable method. Therefore, we develop the multiple quadratic auxiliary variable approach to deal with coupled systems and construct
high-accuracy structure-preserving schemes for the equation. To fix the idea, we first
apply the multiple quadratic auxiliary variable approach to the equation and obtain
an equivalent system that possesses the original energy and mass. Then, a family of
high-accuracy structure-preserving schemes that can conserve the mass and energy is
derived by applying the Gauss collocation method and sine pseudo-spectral method
to approximate the system in time and space. The given schemes have high-accuracy
in time and can both inherit the mass and Hamiltonian energy of the system. Ample
numerical results are given to confirm the accuracy and conservation of the developed
schemes at last.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2023-0137},
url = {http://global-sci.org/intro/article_detail/aamm/24287.html}
}