摘要
In this paper,we propose two new explicit multi-symplectic splitting methods for the nonlinear Dirac(NLD)equation.Based on its multi-symplectic formulation,the NLD equation is split into one linear multi-symplectic system and one nonlinear infinite Hamiltonian system.Then multi-symplectic Fourier pseudospectral method and multi-symplectic Preissmann scheme are employed to discretize the linear subproblem,respectively.And the nonlinear subsystem is solved by a symplectic scheme.Finally,a composition method is applied to obtain the final schemes for the NLD equation.We find that the two proposed schemes preserve the total symplecticity and can be solved explicitly.Numerical experiments are presented to show the effectiveness of the proposed methods.
基金
the open foundations of State Key Laboratory of High Performance Computing and State Key Laboratory of Aerodynamics.Y.C.gratefully acknowledges support from NUDT’s Innovation Foundation(Grant No.B110205)
H.Z.was supported by the Natural Science Foundation of China(Grant No.11301525).
