中国物理B ›› 2016, Vol. 25 ›› Issue (11): 110201-110201.doi: 10.1088/1674-1056/25/11/110201
• GENERAL • 下一篇
Conformal structure-preserving method for damped nonlinear Schrödinger equation
Hao Fu(傅浩), Wei-En Zhou(周炜恩), Xu Qian(钱旭), Song-He Song(宋松和), Li-Ying Zhang(张利英)
- 1 College of Science, National University of Defense Technology, Changsha 410073, China;
2 School of Mathematical Science, China University of Mining and Technology, Beijing 100083, China
Conformal structure-preserving method for damped nonlinear Schrödinger equation
Hao Fu(傅浩)1, Wei-En Zhou(周炜恩)1, Xu Qian(钱旭)1, Song-He Song(宋松和)1, Li-Ying Zhang(张利英)2
- 1 College of Science, National University of Defense Technology, Changsha 410073, China;
2 School of Mathematical Science, China University of Mining and Technology, Beijing 100083, China
摘要： In this paper, we propose a conformal momentum-preserving method to solve a damped nonlinear Schrödinger (DNLS) equation. Based on its damped multi-symplectic formulation, the DNLS system can be split into a Hamiltonian part and a dissipative part. For the Hamiltonian part, the average vector field (AVF) method and implicit midpoint method are employed in spatial and temporal discretizations, respectively. For the dissipative part, we can solve it exactly. The proposed method conserves the conformal momentum conservation law in any local time-space region. With periodic boundary conditions, this method also preserves the total conformal momentum and the dissipation rate of momentum exactly. Numerical experiments are presented to demonstrate the conservative properties of the proposed method.
中图分类号: (Ordinary and partial differential equations; boundary value problems)
- 02.60.Lj