Volume 6, Issue 4
Explicit Multi-Symplectic Splitting Methods for the Nonlinear Dirac Equation

Yaming Chen ,  Songhe Song and Huajun Zhu

10.4208/aamm.2013.m278

Adv. Appl. Math. Mech., 6 (2014), pp. 494-514.

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  • Abstract

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.

  • History

Published online: 2014-06

  • AMS Subject Headings

65M06, 65M70

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