四川师范大学学报（自然科学版）2025，Vol.48Issue(5)：693-703,11.DOI:10.3969/j.issn.1001-8395.2025.05.009
维分数阶强耦合薛定谔方程的保结构方法
Structure-preserving Method for Strongly Coupled Two-dimensional Fractional Schrodinger Equations
摘要
Abstract
The main contribution of this paper is to construct an effective numerical method for preserving the original invariants of the strongly coupled fractional Schrödinger equations.Firstly,the strongly coupled fractional Schrödinger equations are rewritten into an equivalent Hamiltonian form by using the order reduction technique and the real and imaginary part separation methods.Then,the Fou-rier pseudo-spectral method and a variety of partitioned average vector field(PAVF)methods are used in the spatial and temporal di-rections,respectively,and the corresponding fully discrete numerical methods are established.Theoretical and numerical results show that these obtained PAVF methods can preserve the original energy of the studied model,but only the PAVF-P method can preserve the original energy and mass.关键词
哈密顿系统/耦合薛定谔方程/平均向量场方法/Fourier谱法Key words
Hamiltonian system/coupled Schrödinger equation/average vector field method/Fourier pseudo-spectral method分类
数理科学引用本文复制引用
谭凤,冉茂华,刘洋..维分数阶强耦合薛定谔方程的保结构方法[J].四川师范大学学报（自然科学版）,2025,48(5):693-703,11.基金项目
国家自然科学基金青年基金(11801389)和四川省科技计划项目(2024NSFSC0441) （11801389）
