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Volume 9, Issue 4
Structure-Preserving Wavelet Algorithms for the Nonlinear Dirac Model

Xu Qian, Hao Fu & Songhe Song

DOI: 10.4208/aamm.2016.m1463

Adv. Appl. Math. Mech., 9 (2017), pp. 964-989.

Published online: 2018-05

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  • Abstract

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.

  • Keywords

Structure-preserving, wavelet collocation, conservation laws, nonlinear Dirac equation.

  • AMS Subject Headings

35Q41, 65D30, 65Z0

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{AAMM-9-964, author = {Qian , XuFu , Hao and Song , Songhe}, title = {Structure-Preserving Wavelet Algorithms for the Nonlinear Dirac Model}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {9}, number = {4}, pages = {964--989}, abstract = {

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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2016.m1463}, url = {http://global-sci.org/intro/article_detail/aamm/12185.html} }
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 -

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.

Qian , XuFu , Hao and Song , Songhe. (2018). Structure-Preserving Wavelet Algorithms for the Nonlinear Dirac Model. Advances in Applied Mathematics and Mechanics. 9 (4). 964-989. doi:10.4208/aamm.2016.m1463
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