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Chin. Phys. B, 2016, Vol. 25(11): 110201    DOI: 10.1088/1674-1056/25/11/110201
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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
Abstract  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.
Keywords:  conformal conservation law      splitting method      conformal momentum-preserving method      damped multi-symplectic formulation  
Received:  02 May 2016      Revised:  05 July 2016      Accepted manuscript online: 
PACS:  02.60.Lj (Ordinary and partial differential equations; boundary value problems)  
  02.60.-x (Numerical approximation and analysis)  
  02.60.Cb (Numerical simulation; solution of equations)  
  02.70.Bf (Finite-difference methods)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11571366, 11501570, and 11601514) and the Open Foundation of State Key Laboratory of High Performance Computing of China (Grant No. JC15-02-02).
Corresponding Authors:  Hao Fu     E-mail:  fuhaosnsn@126.com

Cite this article: 

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) Conformal structure-preserving method for damped nonlinear Schrödinger equation 2016 Chin. Phys. B 25 110201

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