Local Structure-Preserving Algorithms for the Klein-Gordon-Zakharov Equation

• Published in: Acta mathematica scientia Vol. 43; no. 3; pp. 1211 - 1238
• Main Authors: Wang, Jialing, Zhou, Zhengting, Wang, Yushun
• Format: Journal Article
• Language: English
• Published: Singapore Springer Nature Singapore 01.05.2023; School of Mathematics and Statistics,Nanjing University of Information Science & Technology,Nanjing 210044,China%Jiangsu Key Laboratory of NSLSCS,School of Mathematical Sciences,Nanjing Normal University,Nanjing 210023,China
• Subjects: Analysis; Mathematics; Mathematics and Statistics; Klein-Gordon-Zakharov (KGZ) equation; local preservation law; local energy-preserving algorithms; multi-symplectic algorithms; 65M06; 65L12; local momentum-preserving algorithms; 65M12; Klein-Gordon-Zakharov(KGZ)equation
• ISSN: 0252-9602; 1572-9087
• DOI: 10.1007/s10473-023-0313-2

In this paper, using the concatenating method, a series of local structure-preserving 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.