LOCAL STRUCTURE-PRESERVING ALGORITHMS FOR THE KLEIN-GORDON-ZAKHAROV EQUATION*

doi:10.1007/s10473-023-0313-2

数学物理学报(英文版) ›› 2023, Vol. 43 ›› Issue (3): 1211-1238.doi: 10.1007/s10473-023-0313-2

LOCAL STRUCTURE-PRESERVING ALGORITHMS FOR THE KLEIN-GORDON-ZAKHAROV EQUATION^*

Jialing Wang¹, Zhengting Zhou¹, Yushun Wang^2,†

1. School of Mathematics and Statistics, Nanjing University of Information Science & Technology, Nanjing 210044, China;;
2. Jiangsu Key Laboratory of NSLSCS, School of Mathematical Sciences,Nanjing Normal University, Nanjing 210023, China

收稿日期:2021-10-22 修回日期:2022-02-09 出版日期:2023-06-25 发布日期:2023-06-06
通讯作者: ^† Yushun wang, E-mail: wangyushun@njnu.edu.cn
作者简介:Jialing Wang, E-mail: wjl19900724@126.com;Zhengting Zhou, E-mail: 2276508729@qq.com
基金资助:
National Natural Science Foundation of China (11801277, 11771213, 12171245).

LOCAL STRUCTURE-PRESERVING ALGORITHMS FOR THE KLEIN-GORDON-ZAKHAROV EQUATION^*

Jialing Wang¹, Zhengting Zhou¹, Yushun Wang^2,†

1. School of Mathematics and Statistics, Nanjing University of Information Science & Technology, Nanjing 210044, China;;
2. Jiangsu Key Laboratory of NSLSCS, School of Mathematical Sciences,Nanjing Normal University, Nanjing 210023, China

Received:2021-10-22 Revised:2022-02-09 Online:2023-06-25 Published:2023-06-06
Contact: ^† Yushun wang, E-mail: wangyushun@njnu.edu.cn
About author:Jialing Wang, E-mail: wjl19900724@126.com;Zhengting Zhou, E-mail: 2276508729@qq.com
Supported by:
National Natural Science Foundation of China (11801277, 11771213, 12171245).

摘要/Abstract

摘要： In this paper, using the concatenating method, a series of local structure-preserv-ing algorithms are obtained for the Klein-Gordon-Zakharov equation, including four multi-symplectic algorithms, four local energy-preserving algorithms, four local momentum-preserving algorithms; of these, local energy-preserving and momentum-preserving algorithms have not been studied before. The local structure-preserving algorithms mentioned above are more widely used than the global structure-preserving algorithms, since local preservation algorithms can be preserved in any time and space domains, which overcomes the defect that global preservation algorithms are limited to boundary conditions. In particular, under appropriate boundary conditions, local preservation laws are global preservation laws. Numerical experiments conducted can support the theoretical analysis well.

关键词: Klein-Gordon-Zakharov (KGZ) equation, local preservation law, local momentum-preserving algorithms, multi-symplectic algorithms, local energy-preserving algorithms

Abstract: In this paper, using the concatenating method, a series of local structure-preserv-ing algorithms are obtained for the Klein-Gordon-Zakharov equation, including four multi-symplectic algorithms, four local energy-preserving algorithms, four local momentum-preserving algorithms; of these, local energy-preserving and momentum-preserving algorithms have not been studied before. The local structure-preserving algorithms mentioned above are more widely used than the global structure-preserving algorithms, since local preservation algorithms can be preserved in any time and space domains, which overcomes the defect that global preservation algorithms are limited to boundary conditions. In particular, under appropriate boundary conditions, local preservation laws are global preservation laws. Numerical experiments conducted can support the theoretical analysis well.

Key words: Klein-Gordon-Zakharov (KGZ) equation, local preservation law, local momentum-preserving algorithms, multi-symplectic algorithms, local energy-preserving algorithms

Jialing Wang, Zhengting Zhou, Yushun Wang. LOCAL STRUCTURE-PRESERVING ALGORITHMS FOR THE KLEIN-GORDON-ZAKHAROV EQUATION^*[J]. 数学物理学报(英文版), 2023, 43(3): 1211-1238.

Jialing Wang, Zhengting Zhou, Yushun Wang. LOCAL STRUCTURE-PRESERVING ALGORITHMS FOR THE KLEIN-GORDON-ZAKHAROV EQUATION^*[J]. Acta mathematica scientia,Series B, 2023, 43(3): 1211-1238.

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LOCAL STRUCTURE-PRESERVING ALGORITHMS FOR THE KLEIN-GORDON-ZAKHAROV EQUATION^*

LOCAL STRUCTURE-PRESERVING ALGORITHMS FOR THE KLEIN-GORDON-ZAKHAROV EQUATION^*

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