A novel energy-preserving scheme for the coupled nonlinear Schrodinger equations

作者：Mu, Zhenguo; Li, Haochen; Wang, Yushun^*

来源：International Journal of Computer Mathematics, 2018, 95(1): 61-81.

DOI：10.1080/00207160.2017.1417590

• Coupled nonlinear Schrodinger equations
• energy-preserving scheme
• Galerkin spectral element method
• energy method
• error estimate

This paper explores an efficient energy-preserving scheme for the coupled nonlinear Schrodinger system with emphasis on preserving the Hamiltonian structure based on the weak formulation of the system. First, the Schrodinger system is discretized in spatial direction by the Galerkin spectral element method, and the resulting semi-discrete system is rewritten as a finite-dimensional canonical Hamiltonian system. Second, we apply the energy method to discretize the resulting ordinary differential equations in time direction and obtain an efficient conservative scheme. Using the energy method, an error estimate without any restriction on the grid ratio is derived, and the new scheme is convergent with the order O(tau(2) + h(2)) in the discrete L-2-norm, where tau and h denote the time and the space steps, respectively. Finally, comprehensive numerical results including comparisons with the semi-explicit multi-symplectic Euler-box and the Crank-Nicolson finite difference method are given to illustrate the superiority of the proposed energy-preserving scheme.

• 出版日期2018
• 单位北京大学; 南京师范大学