摘要
In this paper,we propose a conformal momentum-preserving method to solve a damped nonlinear Schrodinger(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.
In this paper,we propose a conformal momentum-preserving method to solve a damped nonlinear Schrodinger（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.
基金
Project supported by the National Natural Science Foundation of China(Grant Nos.11571366,11501570,and 11601514)
the Open Foundation of State Key Laboratory of High Performance Computing of China(Grant No.JC15-02-02)
