文献类型：期刊文献

英文题名：Structure-preserving numerical methods for the fractional Schrodinger equation

作者：Wang, Pengde[1];Huang, Chengming[2,3]

第一作者：Wang, Pengde

通讯作者：Huang, CM[1]

机构：[1]Henan Univ Econ & Law, Coll Math & Informat Sci, Zhengzhou 450000, Henan, Peoples R China;[2]Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Hubei, Peoples R China;[3]Huazhong Univ Sci & Technol, Hubei Key Lab Engn Modeling & Sci Comp, Wuhan 430074, Hubei, Peoples R China

第一机构：河南财经政法大学数学与信息科学学院

通讯机构：[1]corresponding author), Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Hubei, Peoples R China.

年份：2018

卷号：129

起止页码：137-158

外文期刊名：APPLIED NUMERICAL MATHEMATICS

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000430902800009)】；

基金：This work was supported by the National Natural Science Foundation of China (No. 11771163) and the China Postdoctoral Science Foundation funded project (No. 2017M620591). The authors wish to thank the anonymous referees for their valuable comments and suggestions which lead to an improvement of this paper.

语种：英文

外文关键词：Fractional Schrodinger equation; Fractional Laplacian; Hamiltonian system; Symplectic method; Generalized multi-symplectic method; Conservation law

摘要：This paper considers the long-time integration of the nonlinear fractional Schrodinger equation involving the fractional Laplacian from the point of view of symplectic geometry. By virtue of a variational principle with the fractional Laplacian, the equation is first reformulated as a Hamiltonian system with a symplectic structure. Then, by introducing a pair of intermediate variables with a fractional operator, the equation is reformulated in another form for which more conservation laws are found. When reducing to the case of integer order, they correspond to multi-symplectic conservation law and local energy conservation law for the classic Schrodinger equation. After that, structure-preserving algorithms with the Fourier pseudospectral approximation to the spatial fractional operator are constructed. It is proved that the semi-discrete and fully discrete systems satisfy the corresponding symplectic or other conservation laws in the discrete sense. Numerical tests are performed to validate the efficiency of the methods by showing their remarkable conservation properties in the long-time simulation. (C) 2018 IMACS. Published by Elsevier B.V. All rights reserved.