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Decompositions of the Kadomtsev-Petviashvili equation and their symmetry reductions |
| Zitong Chen(陈孜童)1,†, Man Jia(贾曼)2, Xiazhi Hao(郝夏芝)3, and Senyue Lou(楼森岳)2 |
1 School of Mathematics and Statistics, Ningbo University, Ningbo 315211, China;
2 School of Physical Science and Technology, Ningbo University, Ningbo 315211, China;
3 College of Science, Zhejiang University of Technology, Hangzhou 310014, China |
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Abstract Starting with a decomposition conjecture, we carefully explain the basic decompositions for the Kadomtsev-Petviashvili (KP) equation as well as the necessary calculation procedures, and it is shown that the KP equation allows the Burgers-STO (BSTO) decomposition, two types of reducible coupled BSTO decompositions and the BSTO-KdV decomposition. Furthermore, we concentrate ourselves on pointing out the main idea and result of Bäcklund transformation of the KP equation based on a special superposition principle in the particular context of the BSTO decompositions. Using the framework of standard Lie point symmetry theory, these decompositions are studied and the problem of computing the corresponding symmetry constraints is treated.
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Received: 01 December 2023
Revised: 24 December 2023
Accepted manuscript online: 04 January 2024
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PACS:
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02.30.Ik
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(Integrable systems)
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02.20.Sv
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(Lie algebras of Lie groups)
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| Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 12235007, 11975131, and 12275144), the K. C. Wong Magna Fund in Ningbo University, and the Natural Science Foundation of Zhejiang Province of China (Grant No. LQ20A010009). |
Corresponding Authors:
Zitong Chen
E-mail: reyuansar@icloud.com
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Cite this article:
Zitong Chen(陈孜童), Man Jia(贾曼), Xiazhi Hao(郝夏芝), and Senyue Lou(楼森岳) Decompositions of the Kadomtsev-Petviashvili equation and their symmetry reductions 2024 Chin. Phys. B 33 030201
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