TY - JOUR
T1 - Structure-Preserving Wavelet Algorithms for the Nonlinear Dirac Model
AU - Qian , Xu
AU - Fu , Hao
AU - Song , Songhe
JO - Advances in Applied Mathematics and Mechanics
VL - 4
SP - 964
EP - 989
PY - 2018
DA - 2018/05
SN - 9
DO - http://doi.org/10.4208/aamm.2016.m1463
UR - https://global-sci.org/intro/article_detail/aamm/12185.html
KW - Structure-preserving, wavelet collocation, conservation laws, nonlinear Dirac equation.
AB - <p style="text-align: justify;">The nonlinear Dirac equation is an important model in quantum physics
with a set of conservation laws and a multi-symplectic formulation. In this paper, we
propose energy-preserving and multi-symplectic wavelet algorithms for this model.
Meanwhile, we evidently improve the efficiency of these algorithms in computations
via splitting technique and explicit strategy. Numerical experiments are conducted
during long-term simulations to show the excellent performances of the proposed algorithms
and verify our theoretical analysis.</p>