Decompositions of the Kadomtsev-Petviashvili equation and their symmetry reductions

doi:10.1088/1674-1056/ad1a96

中国物理B ›› 2024, Vol. 33 ›› Issue (3): 30201-030201.doi: 10.1088/1674-1056/ad1a96

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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

收稿日期:2023-12-01 修回日期:2023-12-24 接受日期:2024-01-04 出版日期:2024-02-22 发布日期:2024-02-29
通讯作者: Zitong Chen E-mail:reyuansar@icloud.com
基金资助:
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).

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

Received:2023-12-01 Revised:2023-12-24 Accepted:2024-01-04 Online:2024-02-22 Published:2024-02-29
Contact: Zitong Chen E-mail:reyuansar@icloud.com
Supported by:
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).

摘要/Abstract

摘要： 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.

关键词: Kadomtsev-Petviashvili (KP) equation, decomposition, Bäcklund transformation, symmetry reduction

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.

Key words: Kadomtsev-Petviashvili (KP) equation, decomposition, Bäcklund transformation, symmetry reduction

中图分类号: (Integrable systems)

02.30.Ik

02.20.Sv (Lie algebras of Lie groups)

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[J]. 中国物理B, 2024, 33(3): 30201-030201.

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[J]. Chin. Phys. B, 2024, 33(3): 30201-030201.

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Decompositions of the Kadomtsev-Petviashvili equation and their symmetry reductions

Decompositions of the Kadomtsev-Petviashvili equation and their symmetry reductions

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