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Explicit Multi-Symplectic Splitting Methods for the Nonlinear Dirac Equation

Published online by Cambridge University Press:  03 June 2015

Yaming Chen ,
Songhe Song  and
Huajun Zhu
Yaming Chen*
Affiliation:
Department of Mathematics and System Science and State Key Laboratory of High Performance Computing, National University of Defense Technology, Changsha 410073, China
Songhe Song*
Affiliation:
Department of Mathematics and System Science and State Key Laboratory of High Performance Computing, National University of Defense Technology, Changsha 410073, China
Huajun Zhu*
Affiliation:
State Key Laboratory of Aerodynamics, China Aerodynamics Research and Development Center, Mianyang 621000, China
*
Email: chenym-08@163.com
Corresponding author. Email: shsong@nudt.edu.cn
Email: hjzhu@skla.cardc.cn
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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.

Keywords

65M0665M70Nonlinear Dirac equationmulti-symplectic methodsplitting methodexplicit method
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 6 , Issue 4 , August 2014 , pp. 494 - 514
Copyright
Copyright © Global-Science Press 2014

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