Structure-Preserving Wavelet Algorithms for the Nonlinear Dirac Model (Advances in Applied Mathematics and Mechanics, 2018)
The nonlinear Dirac equation is an important model in quantum physicswith a set of conservation laws and a multi-symplectic formulation. In this paper, wepropose energy-preserving and multi-symplectic wavelet algorithms for this model.Meanwhile, we evidently improve the efficiency of these algorithms in computationsvia splitting technique and explicit strategy. Numerical experiments are conductedduring long-term simulations to show the excellent performances of the proposed algorithmsand verify our theoretical analysis.