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.
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).
