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Dynamics of lump chains for the BKP equation describing propagation of nonlinear waves |
| Zhonglong Zhao(赵忠龙)1,†, Lingchao He(和玲超)2, and Abdul-Majid Wazwaz3 |
1 School of Mathematics, North University of China, Taiyuan 030051, China;
2 College of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China;
3 Department of Mathematics, Saint Xavier University, Chicago, IL 60655, USA |
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Abstract A large member of lump chain solutions of the (2+1)-dimensional Bogoyavlenskii-Kadomtsev-Petviashvili (BKP) equation are constructed by means of the τ-function in the form of Grammian. The lump chains are formed by periodic arrangement of individual lumps and travel with distinct group and velocities. An analytical method related dominant regions of polygon is developed to analyze the interaction dynamics of the multiple lump chains. The degenerate structures of parallel, superimposed, and molecular lump chains are presented. The interaction solutions between lump chains and kink-solitons are investigated, where the kink-solitons lie on the boundaries of dominant region determined by the constant term in the τ-function. Furthermore, the hybrid solutions consisting of lump chains and individual lumps controlled by the parameter with high rank and depth are investigated. The analytical method presented in this paper can be further extended to other integrable systems to explore complex wave structures.
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Received: 28 November 2022
Revised: 30 December 2022
Accepted manuscript online: 06 January 2023
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PACS:
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05.45.Yv
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(Solitons)
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02.30.Jr
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(Partial differential equations)
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02.30.Ik
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(Integrable systems)
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| Fund: Project supported by the National Natural Science Foundation of China (Grant No. 12101572) and the Research Project Supported by Shanxi Scholarship Council of China (Grant No. 2020-105). |
Corresponding Authors:
Zhonglong Zhao
E-mail: zhaozlhit@163.com,zhaozl@nuc.edu.cn
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Cite this article:
Zhonglong Zhao(赵忠龙), Lingchao He(和玲超), and Abdul-Majid Wazwaz Dynamics of lump chains for the BKP equation describing propagation of nonlinear waves 2023 Chin. Phys. B 32 040501
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