Symplectic schemes and symmetric schemes for nonlinear Schr¨odinger equation in the case of dark solitons motion  

作　　者：Yiming Yao Miao Xu Beibei Zhu Quandong Feng 

机构地区：[1]College of Science,Beijing Forestry University Beijing 100083,P.R.China [2]School of Mathematics and Physics University of Science and Technology Beijing Beijing 100083,P.R.China

出　　处：《International Journal of Modeling, Simulation, and Scientific Computing》2021年第6期150-167,共18页建模、仿真和科学计算国际期刊（英文）

基　　金：This work was supported by the Fundamental Research Funds for the Central Universities(Nos.2018ZY14,2019ZY20 and 2015ZCQ-LY-01);Beijing Higher Education Young Elite Teacher Project(YETP0769);the National Natural Science Foundation of China(Grant Nos.61571002,61179034 and 61370193).

摘　　要：In this paper,symplectic schemes and symmetric schemes are presented to simulate Nonlinear Schrodinger Equation(NLSE)in case of dark soliton motion.Firstly,by Ablowitz–Ladik model(A–L model),the NLSE is discretized into a non-canonical Hamiltonian system.Then,different kinds of coordinate transformations can be used to standardize the non-canonical Hamiltonian system.Therefore,the symplectic schemes and symmetric schemes can be employed to simulate the solitons motion and test the preservation of the invariants of the A–L model and the conserved quantities approximations of the original NLSE.The numerical experiments show that symplectic schemes and symmetric schemes have similar simulation effect,and own significant superiority over non-symplectic and non-symmetric schemes in long-term tracking the motion of solitons,preserving the invariants and the approximations of conserved quantities.Moreover,it is obvious that coordinate transformations with more symmetry have a better simulation effect.

关 键 词：Symplectic schemes symmetric schemes nonlinear Schr¨odinger equation dark solitons motion Ablowitz–Ladik model 

分 类 号：O17[理学—数学]